The 4L80e is Far superior to the 700r4. In fact if you are running a 700r4 I would question if it would even live long with your 37" tires. Like I said, GM never put a 700r4 in a 3/4 ton, so you either have a th400, a rebadged 1/2 ton (you have 8-lug axles so probably not the case), somebody made a poor decision on a swap, or you have a 4L80e (probably/hopefully the case).
Does your Sub have overdrive? If yes, then rule out the th400 as it is only a 3 speed tranny. Also as previously mentioned, climb under the truck and count the trans pan bolts &/or look for large electrical plugs on the trans body (the 4L80e is electronically controlled by the PCM).
Good Luck!