In aircraft they won't certify a brazed frame as brazing induces cracks in 4130/class materials, obviously not a problem in bikes, but the edge on science is with welding. Gas welding works just as well structurally and is fine in aircraft, but it is harder to keep straight, which apparently isn't such a big deal at 150 knots.

TIG is lighter, because the amount of material required to make the weld, is smaller, and because butted tubes are not required, though in many cases they are used.

TIG has a smaller heat affected zone, but brazing uses lower temps. Doesn't really mater since the tubing is produced with these factors in mind.

TIG uses higher heat than brazing, but it doesn't mater as above.

I doubt there are really any bike metals that can't be TIGged, though manufacturers say that seemingly to delay roll out of their materials, because next thing you know it can be TIGged.

A lot of high production lines that use welding, use robotic MIG, or they use power feed TIG.

Good Tig set costs 4 grand and might break when the warranty is up, you can pick up a decent torch for 40-200 bucks.

Any monkey can make a brazed joint that looks good, first time, if they are lucky, usually some will be nice others, not; TIG is very hard to learn, and very harder still to self teach. I am still using my first brazing project, from over 10 years ago, My TIG welding is still an unpleasant experience for me, and sometimes the tubes. TIG is more difficult to learn in a classroom setting, than brazing, but it is much easier in that setting, because just dialing in the variables in your own shop is very complicated. If someone hands you everything in a ready to go, the welder went for a coffee setting, you will not have as much trouble. However relative difficulty is a nothing since once any process is learned, it no longer maters that it is difficult for someone else to learn, pros own all that stuff.

Culturally brazing has more of that euro flavour, TIG often for people who come up through MTBs, or other machine shop processes.

TIG will do AL, Stainless, Ti, and C steels.

Both allow aesthetic expressions, I think brazing looks better under paint, and TIG looks better raw. Generally people don't understand what they are seeing in a weld, and in some cases the welding is nasty enough to be something you don't want to look at.

If you go to places that don't care, are post modern, they will use brazing, lugs, silver brazing, and welding processes, on the same bike, just depends one what they are putting down.