I had a Thunderbird before the CTX, and I actually think the CTX has lighter handling. Not that the Bird was bad, I just like the CTX better -- very neutral to me.
That being said, all bikes do have different handling characteristics. Sometimes it's just a matter of getting used to the uniqueness of the ride. I've got over 2400 miles on mine, and I still haven't really flogged it very hard as I don't yet find myself completely 'at one' with it, though I can feel that getting closer with every ride.
If you want to talk about a bike pulling down, you should try a ST1300. More than any bike I've ever owned, that one required a truly conscious effort to pull it back up from a lean. Again, not bad, because it was a great handling machine, but it definitely required getting used to.