Mere brazing the crack closed will be most likely a short term repair. Getting the two faces completely clean will be the first challenge. Remember that brass (or actually bronze fillers) are not as strong as the steel is. So unless a build up is done the braze will be the proverbial weak link. And if there were any contributing factors (like misalignment or bent/broken axles) that are not fully dealt with...

Replacing the drop out is by FAR the best repair, and the only one I would consider. Here though there is likely to be much more work and material involved. If a exact dup of the drop out can be found (and will probably be found as a pair) then the amount of stay mods will be minimal. If not then the stay ends (both seat and chain) will have far more modifying to ensure proper wheel placement for alignment as well as engagement to allow for good brazing joinery.

I have done a number of these repairs over the years, this breakage point is the most common for a rear drop out. There have been a few times where the lining up of the stay ends. the drop out tabs, the two slots (and therefore the wheel sitting properly in line) just didn't work out and both drop outs ended up being replaced.

I love it when those who don't do this kind of work say it's a fast and painless job. If the break had been in another location in the drop out I would have a far different view. Andy.