Axel has the same history as Regular Ben, only in the Secret of the Omnitrix saga, Gwen did not survive. He felt it was his fault, and became hardened by it, even until this age.
He weilds the Delta Omnitrix, which is the Dimension 6 equivalent of the Omnitrix MIII. It is unknown how many aliens he has unlocked, however he appears to have similar aliens to Ben.
Ben 10: Dimensional Warriors
We will assume Axel has all the same aliens unlocked that Ben does, so this will be a list of used aliens. They are listed in order of appearance. Axel's aliens all have a similar appearance to Ben's, the only change being green to purple.