I'd get the TA01 for a 20" or 18" barreled rifle because of its fine crosshair "christmas tree" reticle is great for precision shooting but not so good for CQB, and the TA31 for a carbine because of BAC. TA01 series is the only one without the BAC feature, which allows you to keep both eyes open and use the donut/triangle/chevron as a reflex sight, so bright is the fiber optic lit reticle.
If you can only have one, save your money and get a TA31.
New arguy posted a thread re: making the TA01 into something like a BAC equipped ACOG, it involves an Aimpoint and a mount that positions it directly in front of the TA01. All said, that solution will cost you about $550 above the cost of the TA01 (340 for aimpoint, 190 for the KAC offset mount). So why not get a TA31 or TA11 to begin with, unless you actually already have the KAC mount and Aimpoint in your toys inventory.