Dudley is one of those rare characters where both Ultras are quite good, so sometimes I agonize over which one to choose once the opponent has chose their character.
So far, my rule of thumb is to go for U1 if the opponent has some move with 8F+ of recovery that tends to be abused because of the range or pushback and U2 if otherwise to maximize combo damage.
To clarify this, I’ll post some characters and my ultra of choice. If you have good reasons to choose another ultra, post them.
Shotos. Easy. U1 to punish any sweep or fireball attempt.
Sagat. Ditto, although timing is tighter.
Guile. Not sure in this one, since reacting to sonic boom is really hard, so I prefer to maximize combo damage with U2.
Boxer. U2, which may catch some dashing special.
T.Hawk, Zangief. U2 for combo followups only. U2 may discourage Condor Dive.
Hakan. U1 to really make them think twice about Oil Shower.
Cammy, Decapre. U2, although not very convinced.