I don't own a Ti bike but I have ridden a few and will get a Ti bike for a second bike. A well made carbon bike will last longer than its owner. Carbon bikes are light and do a nice job of eliminating road buzz. Also, carbon bikes can be repaired easier than a Ti bike. However, not all carbon bikes are created the same and some are more crash tollerant than others.

If you have the budget, both are good options but if I could only have one bike it wold be carbon fiber.