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.
2014 surly straggler
2012 surly moonlander
14 badboy 14 carbon beargrease 13 jones spaceframe 14 straggler, 05 pugsley, 13 pugsley, 12 moonlander, 13 krampus x2, 13 fargo 2, 11 surly pugsley, 01 Volvo Cannondale, 01 dekerf limited, 98 cannondale caad2, 94 san andreas, 96 san andreas, 93 pace rc200 f3, 08 Ti moots rigormootis, 93 Ti merlin xlm, 09 Ti jeff jones spaceframe, 93 fat chance yo eddy (ex dave hemming), 11 salsa mukluk, 00 scott octane, 03 stumpjumper comp, 07 s-works fsr carbon, 08 revolution triad 2, 94 claud butler kylami, 96 cannondale m500, 93 townsend, 07 scott scale 30 carbon, 92 CR dogs bolx, 09 hooligan 1, 99 trek 6500, 10 badboy