More places will do custom titanium.
There are also the hybrids of carbon/ti – Serotta Ottrott, Independent Fabrication Crown Jewel, Seven makes a couple.
Plus a bunch of Ti bikes with a carbon seatstay (I’d consider these a step below the carbon/ti hybrids which usually have two or more carbon tubes with titanium lugs).
Of carbon-only, I know Guru will do custom and so will Calfee.
Weight is pretty close. Carbon is a bit lighter, but in general it is hard to make a carbon bike a lot lighter, because the tubes would be too thin (which is what limits the frame weight on a lot of bikes – ti, steel, and aluminum). Certainly weight won’t be a deal breaker.
Neither one will rust. Carbon might be a tad more comfortable, as a composite will absorb more vibration. Titanium is also VERY good at dampening vibration, however.
The advantage of titanium is that it is “tougher” than carbon. By that, I mean in the strictest material sense. Titanium is a metal, and a very durable one. Carbon is immensely strong, but can also be quite fragile in certain aspects (like you can’t gouge your titanium frame nearly as easily as you can a carbon one. Metal is just plain tougher…)
I don’t think you can go wrong either way. Some people are totally sold on one over the other, but I think a good frame from a good builder will be your best choice, and don’t worry about the material.
My first real roadbike choice was between a Trek 5200 and a Litespeed Tuscany. Both great bikes. In the end, I chose the Litespeed because I just like metal. To this day, if I polish up that frame, it looks as good as new. I think it will always look sexier than a Trek. That’s just me, though…