The impression I've gotten from listening to framebuilders is that the tubing diameter is much more relevant to frame stiffness than the material itself. In other words it's possible to build a stiff steel bike, or a flexible aluminum bike. I think one reason people tend to associate aluminum with a harsh ride is because most aluminum bikes happen to have oversized tubing (maybe due to the material not being as strong as steel). In fact, though, you probably don't actually want a very flexible aluminum bike, because aluminum has a finite lifespan when it comes to flex, unlike steel, so perhaps that too is why most aluminum frames are built quite stiff.

As for Ti, I would assume that it's also possible to build a very stiff or very flexy titanium frame. It's all in the geometry, and a good framebuilder would be able to make it with whatever characteristics you want/need for the application.

Likewise, I don't think lugged vs TIG welded makes any practical difference to the stiffness - you'll see huge discussions about this flame-worthy topic on some forums, but as far as I can tell the technical consensus seems to be that if you're blindfolded (not a good idea on a bike, but metaphorically speaking) then you can't tell the difference. Again, the geometry and tubing type and diameter make the biggest difference. Tubing type - some steels are harder, e.g. Reynolds 853 is very hard, which allows the framebuilder to use thinner tubing without compromising strength. So there are obviously some choices to be made with materials, depending on application.

Neil