Originally the custom builder went for fillets because the lug were road angles and it was hard to build a bike with the right bb height and head angle. you can tweak and road like a degree or two but then you are out of luck. Fillet lets you make any angle and its pretty quick to do in comparison to lugs.(read the Paterek manaul http://www.timpaterek.com/tpmanual.htm
) its the finishing that take longer than making the dam thing.
As for strength and weight. if you make a close fit joint do that the tube miters shows a perfect fit you can use very little rod and make small fillets. like on http://www.enigmabikes.com
small fillets and no real weight gain. If the tube thickness is 1.0mm you can do a fillet that is 4mm in radius and still get full strength so not much more that a tig weld. Smaller if you use a 5% nickle rod. problem with small fillet is they are very hard to finish. Overbury used to use dyna-file then by hand to finish their fillets so it makes sense to make them big so you can get the tool in to file them. Obviously back in the day there was no cad based finite element testing software, so off road probably best to make them a bit bigger right?. big fillets don't damage the tube strength through heat damage but more often but warping the tubes. you can use this to tweak the angles as you build so if you add more fillet to the side of the join when it cools it pulls in that direction.
Older tubes sets were more sensitive to heat and tig welding was often not a strong as fillet brazing. This is not true now, some of the Columbus/ Reynolds tubes lose no strength when welded or even get harder (niobium additive).
Tig welding became the way just out of speed, no fluxing, not pre heating, no flux clean up, no file to finish. but where the fun in that? to me it done matter how its built as long its build well and there some craft put into it. so an 20 year old British built bike with fillets still makes me smile. Hope you find one.