Only you can decide what frame size is best for your needs. Keep in mind implements for 3x20 will be more expensive.
Once into a 3x20 the additional HP of a 3720 will be mostly wasted unless major PTO work is contemplated. As for ground engaging - will probably run out of traction before HP, so whether buying new or used evaluate the $$$ difference compared to HP and see if the extra $$$ are justifiable.
With 3x20 the BH and MMM and FEL can all be mounted at the same time. Especially with Turf Tires it is entirely debatable and depends on the quality of your lawn.as to whether mowing with the BH attached works or not. It's not that difficult to remove the BH or FEL for mowing.
The 3x20 gives you a choice of two BH sizes - 375 & 485. Both are more powerful than the 2xxx BH. In addition to actually digging deeper (7.5' or 8.5') the reach of the BH is longer which provides several advantages, not the least of which is not having to move the tractor as often.
As for MTM's 3120 he has the mid PTO and Power Beyond. The PTO especially, is expensive as a dealer add on. With that tractor you would need the 3rd Rear SCV for use of MMM. On a 3x20 the preferred FEL would be the 300CX.
If not in a rush used 447 / 375 /448 / 485 BH's come on the market from time to time, in fact there is one in Private Party ads for $3,500 plus cost of mounting brackets. Woods and & Wallenstein also make aftermarket BH's to fit the 3x20 series.
Correct me if I'm wrong Cinder but I have never used my power beyond, so I'm not sure. What I understood from the dealer is that it does have a lever operation so it could be used for something like a MMM but could be hooked up to a BH as well. Of course for a little more you could have the right set up and get another remote. As for my loader it is the 300X, not CX. I didn't plan on taking it on and off much and this one was on the dealers lot so I jumped on it. And there is a 485 BH for sale here:
http://www.tractorbynet.com/forums/private-party-ads/226502-john-deere-485-backhoe.html
I've had mine for a couple years now and love it. I just bought more land at my cottage and would like a larger machine. I have a 5410(80HP) and I found myself using the 3120 a lot just because of the maneuverability over it. I just need to keep the 5410 at the farm and another machine for up north so 3120 must go. Willing to make a deal if your interested - I don't want to shove it down your throat though. I understand the "new tractor" appeal:thumbsup: