I have both - actually two shaped-tube titanium bikes and a custom, lugged ENVE-tubed carbon bike.

I have ridden straight tube and butted titanium bikes as well but prefer the Lynskey shaped-tube bikes - lateral stiffness with a slight vertical compliance and high frequency buzz-absorbing. I have ridden only about 7000 miles on them but love every moment on the bikes.

I recently got a custom, lugged ENVE-tubed carbon bike and have only ridden about 500 miles on it. It feels worlds apart from the other monocoque carbon bikes that I have ridden - the ride does not feel as brittle or overly stiff. The road feel is not as springy as the Lynskeys but just as nice. However, the custom geometry fits me like a glove so it is hard to separate the material feel of Titanium and ENVE carbon tubes and the custom geometry set-up of the custom, lugged ENVE-tubed carbon bike.

So, as long as you are comparing equally classed titanium bikes and similarly constructed carbon bikes, the difference would be minor and probably only felt after at least 5000 miles and after 3-4 continuous hours on each bike.

Mark