No, not really. Isn't the opening quote in the rematch like, 'thanks for coming to lose to me' or something? He's still got that smug arrogance, plus he's kind of dickish in the phone calls as I recall. He's obviously grown up a bit since the Gen 1 story though, so obviously he's toned it down a bit, but out of character? I don't agree.
You've also got to remember that while Red was his rival, the Gen 2 protag is just some random trainer from Johto - he isn't going to trash talk as much since their isn't any history or anything really personal behind their battles.