I have owned some nice Ti bikes and a couple of nice carbon framed bikes...
I'm a heavy dude, not a technical rider but can at times have a bit fun and treat a bike to a hard ride, never had an issue with either materials, in frames or components.
Both bikes will be stiff and light, the Ti absorbs shocks without you knowing it, but then again, carbon isn't as harsh as aluminium I found.
If your not a massive keen rider, either is a good choice, go with a decent budget though, exotic frames can vary hugely, from £400 to £5,000 with my experience, but can often ride similar!
They have to be mated with decent spec kit to get the most from them, otherwise you might as well have a decent steel frame.