I build fillet braze bikes, so I am biased. I think TIG looks unfinished and boring. Fillet brazing is my favorite because you aren't limited by angles and tube diameters but you still get a very neat finished look.

as far as deformation and coldsetting goes...it all depends on the builder. A good builder will know a process that will stop the frame from deforming or twisting with either joining process. I will usually check my frame after tacking to see if I need to pull a joint in a certain direction or keep it in place during brazing.

either way, you will get an awesome bike. both ways are plenty strong if done correctly. ask you builder their opinion.