radman,
I have had both these machines. In fact, I have had two 3720's among my many tractors. I now have a little 2320 and although my tractoring buddies laugh at me, it is about my favorite to operate of all. With regard to the 4520, it is MUCH more tractor than the 3720. The difference in almost all areas of performance is notable. I really like the size of the 3720, but in reality the 4520 is not that much larger in actual "taking up space" size, but it looks HUGE compared with a 3000 series. The kicker is transporting it. Because it is so large and has larger tires, a fully-ballasted 4000 series machine can be a challenge to haul, unless one has a 3/4 ton or larger truck. If your machine is likely to stay put in one location, then it is a great choice. There IS a major difference in ground clearance. High centering can happen but it is not likely. As for the tires, R4 tires on any machine are simply not adequate for very muddy conditions, or icy based snow. They have very firm sidewalls and primarily are meant to not distort under heavy loads and wear well. Ballasting does help, even in mud, but the difference is not that notable. R1 tires, on any machine, will markedly improve traction. Thus, if you decided to keep your 3720 and went with R1 tires, your problem would get much better. It would be better still on a larger, higher machine like a 4520. I cannot attest to whether a 4520 would get a great deal better traction with R1's but can say I did switch my R4's to R1's on my last 3720. It would pull my box blade up our steep slippery gravel drive better with unloaded R1's than with loaded R4's. The only downside to R1 tires in either a 3000 or 4000 series machine is that if one does load them they are so narrow they do not hold a great deal of liquid ballast v. the wider R4 so weights might also be needed.
My thought is that even spending for a wheel and tire combo, you are likely to come out better not taking a large hit trading in your 3720 and when you do go to sell your machine, having two sets of wheels and tires might be a strong selling point. I think your current machine would perform better and closer to your expectation with a tire switch only. If you are just really looking to trade, the 4000 series tractors are more capable, but at a price. One often does not realize just how much larger they are (although their footprints aren't that much different) until one sees a 3000 and 4000 side by side. Going to a 4520 with R4 tires likely will not totally solve your problem and you will be poorer for it and still not totally happy without a tire upgrade. As for a 4520 v. a 4720, this is personal choice. I would argue for ground engagement work and non-pto work a 4120 is as good as a 4720. Both these machines have more power than grip, and I would strongly doubt a 4720 would outperform a 4120 in this case. Most of what a buyer gets with a 4720 or 4520 is more PTO HP to power implements which may tax the engine and the cache' of having the top end machine(s). Just a thought.....because a lower HP 4000 series machine would come a bit closer to price than the big HP ones. Keep in mind the engine, hydraulics and most attachments are exactly the same among the 4000 series.
John M