Pros: Titanium is lighter, stronger, more durable and more (theoretically) comfortable than either carbon or aluminium. Cons: More expensive. Aluminium is the cheapest. Aluminium and carbon have limited lifespans and can't be fixed if they get bent/broke. Titanium can. Actually- it's probably a lot more complicated than that, but that's it in a nutshell. If you want a bike to last years and can afford to splash out on it now, a titanium frame is also likely to be the least expensive in the long term as it could literally, if looked after, last you decades.