Having the opportunity to instruct in an X73 and X51 equipped 996TT, I was very impressed by the cars performance on the track. The AWD was nearly transparent. 450+ hp was nice too

. Certainly no fear of the dreaded "lift-throttle oversteer" of "real" 911s

A GT3 would be more communicative than the TT and would have some lift-throttle oversteer to learn how to control.
That said, the Boxster is a remarkably well balanced car that is enjoyable
despite its comparative lack of hp. I am not suprised you like the Boxster more in this scenario.
As a fairly recent Boxster owner I am torn. I sold a 1978 911 to get the boxster. While it is a tremendous car, it does lack the feel/charm of the 911. The cars are equally fast, they just acheive it differently.