Every method claims it is better, I am just here to say so for TIG. The myths against are that tig is weaker, no skill, cheap. The truth is TIG is the only option of the three that you can use for a certified aircraft weld; harder to do, much steeper learning curve; more expensive gear for a small shop, at an industrial level either can be done, but that isn't really relevant to parse to the nth degree.
Other things are: lighter than brazing , more geometry options than lugs. A good deal of tubing is currently designed specifically for it. There is an art to it, though not universally understood. Tends to be used with better, joints, better fixturing.
A huge one is that it is adaptable to more materials, with the other two metals you are left pretending that Al, and Ti, are... sorta not there. I mean, they are making F-150s out of Aluminum to meet the gas standards. Time to move on.
I'd say that is a pretty convincing list. Even if you happen to prefer the way lugs look, you can tig that together. Some of the fancy bikes that use custom lugs are tigged together. Not sure what role the lugmasters play in making some kind of contribution to TIG. Most TIG guys I know also can do brazing, and lugs. Most name lugmeisters I hear about can't weld. So if you get a bike with TIG on it, there is at least a chance they made a reasoned decision which process to use where. BF being an example of a company that uses all thre processes on the same bike. Or maybe not, I was thinking they sleeved something.
As far as composites are concerned the Chinese can swing it if the market ever develops.
As I said above, there are legitimate opinions on all sides. But only if they actually get out. In general I think the craftspeople know all this stuff, and the sillier stereotypes exist mainly in the popular imagination. That was not always the case in the past. But a guy who actually has industry experience these days probably saw more than lugs at one time.