Your A/B scenario does not reflect how you would actually use a drive on the AXE-FX IMHO - USE a real patch that you would normally use the drive in.
It seems to me, that the only way you can "A/B" anything, is to make the signal path identical. Because the global gate is first in series of all other blocks on the AXE-FX II, (even in the drive only scenario you have described - that is unless you disabled the gate) and because your drive on the AXE-FX may not be first in your other normal patches, to accurately A/B your drive, you need to put in an effect LOOP, a send and return either directly in front, or behind the drive(s) which you want to "A/B". And cable your pedal (use short 18"-36" decent quality cables)Then turn on the this "Effect Loop", with the drive Bypassed as your "B". Then Bypass the "Effect Loop", with the drive Activated as your "B". This would give you a true "A/B" environment. Try it. It is up to you to experiment with your "A" drive on the AXE-FX II to get it dialed in correctly. It wont just work with your perfect tone as we all have different likes in this arena. Not until it is dialed in, just like with any Analog pedal First identify to few parameters on your "B" drive and notice their counterpart on the "A" drive. You should be able to approximate the "B" drive and gain some understanding of the AXE-FX II drive structure when you give a reasonable amount of time. Consider this experimentation as a Time Investment into your tone.
The Platinum lining to your cloud will become apparent at that moment when you get past thinking that what you are doing is copying your old. limited analog pedal, and that you now get to take the old concept and keep going with it. As you realize you can take what started as copying a tone, and now you are creating your own signature drive tone. I find huge power in lower mix levels when going for smooth lower gain tones (subtle can be better than in your face with the drives IMHO) and on higher gain settings, watch that level, crank that gain, then sculpt it with the drive eq. Then, as M@ and others have said, try stacking with PEQ and/or even cascading drives once you feel comfortable with your ability to control and understand your digital drive realm, Then, stop looking back at how you USED TO make your tone, and begin to see the power in what you now can do which dwarfs the limits and issues of your OLD basic drives.
Or, with the power of the AXE-FX II's routing abilities, set up a loop and use your OLD Analog boxes to your heart's content. The message here is that you can do whatever you want now that you own an AXE-FX .
As said before,...... have fun, as this is not a problem, it is actually a door that leads to killer new tones if you like...