I always wondered what the in-story reason for Dante's DT's being different depending on the weapon might be. Too bad that didn't carry over into DMC4.
I always assumed that it was because his DMC3 DT was in a "larval stage", not very developed on it's own and susceptible to influence from outside factors, while by DMC4, Dante's grown in his personal power and his Devil form has matured into it's own, Same with DMC2.