The push-push switch changes the scaling or range allowed for the Discrimination control. In one position of the push-push switch you can scale the discrimination range to go from salt water to the rejection of screw caps.  In this position all iron is rejected.  This is considered to be the normal operating position for coin hunting similar to most detectors.
In the second position of the push-push switch, the discrimination range can go from iron accept to the rejection of screw caps.  With the discrimination control counter clockwise many iron objects can now be picked up.  When you choose this position you are in effect expanding the lower limit of your discrimination range.  This is consider to be a relic hunting mode or when you are looking for objects that reside near the response of salt water.  Thin rings for example.     In both positions of the push-push switch the upper limit remains the same.  That is, in the fully clockwise Discrimination control position screw caps should be rejected.  This level of discrimination does not change with the selection of the push-push switch.
The confusion of the filters have to do with the Baron using three parallel double filters.  The extra parallel filtering allows the Baron to incorporate the additional discrimination range when you select "iron accept" with the push-push switch.  The two tone ID also works off of this same circuit.  At the time of the Baron's design this particular discrimination approach was not used in the currently available products.  I felt that it offered the customer greater detector flexibility and performance.
Incidentally, if you install the module with the notch feature then the Baron is operating with four parallel filters.  Keep in mind that the Baron is still a two filter instrument as far ground rejection goes.  The extra filters simply provide multiple discrimination settings or ranges.  Multiple parallel filter processing was not a new concept when the Baron was designed.  I had used this approach in the Teknetics 9000 and 8500B. However, for those products it was not used for the same reason or in exactly the same manner.  One final point.  In the case of Microchip designs like the GoldTrax and CoinTrax Modules parallel filter processing is used extensively to enhance design performance.  It is more expensive to add parallel processing in analog designs such at the Baron.  This is not the case for Microchip designs.

At the time of its introduction we felt that the CoinTrax module would eliminate the need for some of the basic Baron features like the iron accept/reject mode.  Needless to say we made a mistake in that assumption.
As many have observed the Baron with an installed CoinTrax module is just that.  All the original Baron features are still present.  I designed the CoinTrax module several years ago.  As I recall most all of the features are spelled out in the available documentation.  However, the GoldTrax module has several undocumented features.

The BH coils that were build by Teknetics in the 1980's will work fine on the Mark I.  However, the newer BH coils may not work as well or not at all.
One of the best coils ever made by Teknetics was the thin 10 inch coil. It's only about 3/8 inch thick and is white in color

The 9000 and 8500 series were also fine detectors.  But they have limit depth.  Here in Oregon the mineralized ground will limit the detection depth for a 9000/8500 to about 4 or 5 inches.  The Mark will do better than that.
In low mineralized ground the difference is even more.  I used to take a (modified) Mark I with me when I went on trips.  In Mississippi, where I grew up, I was amazed at how well the Mark performed.  I also perferred the Mark's Target ID over the 9000/8500.  The Mark's single sweep ID accuracy reading is far superior to the 9000/8500.

A Baron with a CoinTrax module installed can not be used with any other "front installed" module.  The CoinTrax module becomes the actual detector.  As you observed all the components not needed are removed from the main board.
However modules can still be installed in the back.  Deep Hunter and battery recharge for example.  Discovery will discontinue making modules in the future.  If you are interested in any module you might consider contacting the factory as soon as possible.

The Mark I is really a 1 and 2 filter detector.  The circuit automatically measures the ground mineral magnitude and decides which filter to use.  If for example you make an "air test" on a target it will always use the 1 filter mode.  However, as soon lower the loop to the ground it switches to 2 filters automatically.  It will continually switch between the two based upon the ground mineral strength.

A analog signal can be converted into digital form for processing using "digital signal processing" or DSP for short.  The DSP term is a very general and broad discription for manipulating analog signals digitally.  In many cases using a DSP approach will cut parts count and cost but add little to actual performance.  This is not to say that using DSP is no better than using conventional analog circuitry.  Here is an example.  It is possible to design analog filters in a digital format using what is called IIR filtering.  There is a direct correlation between these two approaches.  If we were to stop here the clear winner would be the analog circuit because it's generally cheaper.  However, there is a lot more to "going digital" than designing analog filters in an IIR digital format.  There are many other types of data manipulation that can be done digitally that can not be done in the analog world.  For example, implementing a FIR filter is easy using DSP but for all practical purposes, impossible in the analog world.
Here is now I look at the advantages of using DSP.  There is a certain amount of analog circuitry required in all metal detectors.  The Oscillator,front-end and audio circuits are analog.  Additional circuitry is required to change the analog target signals into digital for processing.  Once the input signals are within the microchip the degree of filtering, processing or anything else you want to do is only limited by the amount of available chip memory and the designers skill.  It's really quite amazing what can be done.
Before you can answer the question about which is best you must know more about what how the designer is using DSP inside the microchip.  That may come down to how much you trust the manufacture and their engineering crew.

Anytime you add discrimination you might block (reject) targets that you may want.  For example, assume you adjust the discrimination so that a target is not rejected in an air test.  However, if you now bury that same target and try to find it with the discrimination set as before, you might not be able to locate it.  This characteristic is due to the ground mineral effecting the target's phase.  The greater the ground mineralization the worse this problem will be.  The ground mineralization effect may force the target's phase into the discrimination zone where targets are rejected.  Motion detectors like the Baron help reduce the negative effects of the mineral moving good targets into discrimination zones.  However, they are not perfect.  The deeper the target the weaker its signal and greater are the odds that the mineral will distort its phase to the point where it will be discriminated out.  If you want to increase your odds of finding deep targets use the least amount of discrimination possible.  Some will say use zero discrimination and you want miss anything.  That's true, just use the "all metal" mode and you will get everyting.  However, when I designed the Baron I wanted to find a better compromise.  I designed the "iron reject" on the Baron to add the least amount of discrimination possible and still reject most iron.  This will increase your odds of finding coins.

The original Baron detector was designed as a analog (non-digital) circuit on a printed circuit board or pcb. This board, which we call the "Main" board uses the entire space inside the case. The original circuit on the Main board was a totally functioning All Metal and Motion detector. The modules were apart of the original concept. However, at the time it was designed we had no plans to incorporate a microchip into a module or on the Main circuit board. It was only later that we decided to design a Module directed toward gold hunting using a Microchip. The main purpose of the module was All Metal mode operation with AutoTrax ground balancing. This type of design is best done using a Microcontroller or Microchip.The GoldTrax All Metal mode operation was programmed into the microchip. All other detector operation uses the standard analog circuitry on the main printed circuit board. The CoinTrax is completely different from the GoldTrax module. Remember how I said that for the GoldTrax module, detector operation is split between the module and the main board. Well that's not the case with the CoinTrax. The CoinTrax module is a complete metal detector all on that little module board. Except for the loop oscillator, power supply and audio output the circuitry on the main board is not used. The actual metal detector circuitry is on the CoinTrax module board and all the processing is done in the Microchip. The Microchip program completely operates the All Metal and Motion Modes.

Teknetics was started by several individuals who left White's Electronics. Since we had designed the coils at White's we, of course, knew everything about their characteristics. One particular characteristics about the Whites coil that we considered a negative was that the transmit coil was about an inch less than the diameter of the actual housing. At that time the White's transmit coil was about 7 1/4" in diameter. So, we reasoned that our Teknetics coil should have the same transmit diameter but with a newly designed housing. The overall housing diameter would be about 7 1/2". The result would be a coil with equal of better sensitivity (on a given target size and depth) but a physically smaller coil.

As most of you have observed a larger coil will pick-up more ground mineralization. Because of the coil size it is effectively closer to the ground than a smaller coil. Therefore, it may make more sense to use a smaller coil in high mineral. Keep in mind that a coil picks up the ground in a very non- linear way. Pushing the coil down against a high mineral ground may get you say 1/2" closer to the target. However, the increase in ground signal may be several times greater than a deep target's signal. In this case you would wind up with less sensitivity. For better results raise the coil 1 or even 2 inches and use a smaller coil in highly mineralized soils.