I think that if this came down to deciding between several builders the key thing would be to try to make the decision outside of the issue of how the tubes are joined. Aesthetics aside, the real ordering of joinery methods should probably be TIG, Fillet brazing, lug. Somehow it's all backwards. But so is deciding a bike on how the joints are made. Fit, getting the precise kind of bike you need, and your builder's experience should count for more.

On aesthetics i think TIG is also superior, but you won't find too many who agree. The reason is that real art and craft values fingertips. Meaning the human trace left by the master. Like brushstrokes. Not to be confused with someone who can't cover his tracks due to poor workmanship. TIG leaves behind a certain fingertip impression of the builder, it can be perfectly smooth like Don from Anvil, or it can be various kinds of "dimes" (a good deal of it can also be the electronics of the machine). Even where it is perfectly smooth the fillets left behind seem to appeal to some as being too small, people like the beefy look. However these are the only real smooth fillets out there, right from the chraftsman's touch.

While obviously brazing works great, it is hard to see the amount of heat required to build up the brass is an advantage, it's costly, increases your carbon footprint, heats the tubing a lot. But the aesthetic issue is they don't go raw. They file and sand the heck out of the stuff so that the end result is like bondo, no fingerprints. If bondo is what you want, why not bondo tig? I have some welds like that that have been out of doors summer and winter for 5 years and still are great, no lifting of the bondo, nice fat look.

Another option with TIG is the tigged over layer of brass. Very light amps are used to melt brass over the weld to fair it in. Never see this on bikes, and I prefer the fingerprints, but for those who want the melted techique, that is a good part of what the brass is in the welding store is for... I don't expect people to agree, and do accept the beauty of the good conventional bike builder. But I have also been around the craft world a long time, and know what gets respect more broadly and what doesn't.