When should I use Abel's U1, Soulless, and when should I use Abel's U2 Breathless? Like, what are the main differences, online matchmaking wise? I like using Soulless due to Armor Break, but at the same time, U2 has armor and can be held down to delay it. Not sure quite what the differences are. Is one better for a ground-game than the other?
The big difference between Ultra 1 and Ultra 2 is that Ultra 2 (Breathless) is a command grab. You can avoid it by jumping, or using a move that has invincibility, but you cannot block it. The armour allows you use it as an anti-air, assuming their attack doesn't cross-up.
Ultra 1 on the other hand can be blocked, but has two important properties: Firstly it's an armour breaker, secondly it can be easily comboed into with his cr.HP "Elbow launcher". His launcher can in turn be comboed into by (normal) FADCing the first hit of his Change of Direction (QCF+P). Even if you mess up and cancel on block you can try a risky grab or roll.
They both so a similar amount of damage, with soulless having an entirely negligible advantage but being scaled to a lower amount if you combo into it. A raw Ultra 2 will deal more damage, than comboing into ultra 1. This is important because comboing into ultra 1 will be the most likely scenario, compared to ultra 2, which you will likely hit as a mixup (note: it can be jumped out of on reaction) or by using the armour.
In USF4, you have another option: Red focus cancelling into Ultra 2. The first hit of Change of Direction (QCF+P) allows you to hit a red focus into ultra 2.
As for when to use which, it's really a personal choice. Ultra 1 is consistent and you can land it fairly easily in almost every match. Ultra 2 is tricker, but you may want to use it when you suspect a lot of jump-ins. An example of a matchup you may want to use ultra 2 in is Abel vs Yun. Yun may miss-time/miss-space a divekick, leading to a free ultra 2 for you.
Finally, you of course have the option of W-Ultra in USF4.
Edit: A final note on the damage difference (raw U2 vs combo U1): If you only do cr.HP into U1 it still does more damage than a raw U2. The damage of the ultra itself (not the entire combo) will be lower, however. In fact most combos into U1 will deal more damage than either a raw U2 or a combo (EX red focus) ending in U2.