I had a very nice German-made blade welder for a while there, but as many others have noted, heat-treating of the weld was often an issue.
The band material is of course a higher-carbon, hardenable steel, and if cooled too fast, can become brittle. The band must by the nature of the machine be flexible, so a brittle spot leads to another breakage.
Silver brazing is done at a somewhat lower temperature (that is, if done properly) and the silver itself is a malleable (IE, somewhat soft) metal which helps the join last in use.
As noted above, a "scarfed" (that is, tapered) joint will be stronger than a square, butt-welded joint. However, grinding a 'scarfed' joint is more difficult than doing a butt joint. For a square, butt join, you simply put the two ends of the band back to back- the teeth on one end facing to the left, the teeth on the other facing to the right. That way, when you grind the ends at the same time, even if it's not completely square, the angles cancel each other out when you realign them for welding.
Grinding the taper of a scarfed joint is trickier- you can grind both ends at the same time (making sure the teeth face the same way this time) but if you don't grind them perfectly square (or very close to it) the angles don't mesh, and any error is doubled.
However, silver solder has a little tolerance for misalignment or gaps- naturally, the closer the fit, the stronger the weld, but it doesn't have to be 100% perfect.
The other trick is to use an alignment jig that holes the blade ends square to each other (regardless of the end angle) as you solder. Jigs are easy, and there's a dozen different variations online.
I'll also note that the silver brazing is somewhat tricky all by itself. Buy good flux, and if you can find it, I've heard the trick setup is to by flat strips of braze- like .010" thick. Lay it between the blades and just heat. Supposed to be easier than getting it to wick in.