The 2 largest differences between the M1A2C and the TTB are the armour profile and the gun.
The armour profile on the TTB has a smaller but weaker lower front plate (it can still resist 440mm of AP pen on the lower half, and 730mm on the upper half) compared to the M1A2C (~650mm of protection across the entire plate). This can be combined with the TTB's hydraulic suspension to hide your smaller weakspot and give you better overall survivability on the hull front. Additionally, the TTB's turret is both unmanned (meaning it takes less damage when hit) and has better frontal armour than the M1A2C turret (no need to worry about the turret ring weakspot). The one area that the M1A2C does better than the TTB is in side protection, as it gets multi-layered ERA on the hull sides and ERA on the turret. As a result, the M1A2C is better protected against HEAT (especially tandem HEAT) from the sides, and has some protection from low-penetration AP and high-penetration AP that hits the side armour at a >30 degree angle.
The other major difference between the TTB and the M1A2C is the gun. Where the M1A2C gets a conventional single-shot gun with an 8.75 second reload (which can be improved with a researchable breech upgrade and loader skills), the TTB gets an automatically loaded gun firing the same ammunition (same damage and penetration on the stock gun, all shells get an extra 35mm of penetration on the upgraded gun) with a 6-shot ready rack that reloads every 10 seconds, with 4 seconds between shots. Overall, this means that the TTB has respectable stock burst DPM of 8850 with the upgraded AP (8700 with the stock AP) and a sustained DPM of 3540 (3480) compared to the surprisingly good overall DPM of the M1A2C (3977 stock, ~4800 fully upgraded and with loader skills), and that the TTB has a slightly better chance to do damage with the extra 35mm of penetration.
Overall, I'd probably pick the TTB. The burst damage it offers is extremely useful in PvE and allows you to do all of your damage up front and retreat to protect your somewhat questionable armour if need be. Event then, the somewhat questionable armour of the TTB is significantly better than the M1A2C's since most of the vehicles you will be facing will likely be firing AP with enough penetration to punch through the M1A2C's hull front (but not always enough to punch through the middle plate of the TTB) or tandem HEAT ATGMs that will go clean through the hull front of both vehicles or get steered around the ERA on the vehicles' sides and go clean through the side armour. The doesn;t even consider the fact that the TTB gets hydraulic suspension or an unmanned turret, which both significantly improve the TTB's ability to find and make use of hull-down positions. In just about every situation, the armour on the TTB stands up just as well or better than the M1A2C, and the advantage in burst fire means that the TTB doesn't need to spend nearly as long exposing itself to incoming fire to deal damage. Sure, the M1A2C gets decent DPM, but it lacks the much of the protection needed to keep itself alive long enough to make use of that DPM.