I think the older and newer Tecumsehs each have disadvantages, though not the same disadvantages. There is a case for keeping the early Tecumseh (more correctly, Kirby-Lauson) if it is the original engine fitted to your mower from new, just because it maintains originality, which is a virtue to a collector. If your mower originally had a Briggs, it would be good to put an old Briggs on it, for the same reason. However a new Briggs is highly likely to have been made in China, and the experiences of Chinese Briggs engines reported to us so far have not been all that encouraging: the older ones seem to have often been badly built, and even the properly built ones made more recently may not be very durable due to materials issues. "Genuine" Honda engines are now often made in China as well, but we have not been getting multiple reports of them being badly built. Chinese copies of Hondas, known as chondas, seem to be worse than genuine Briggs engines made in China. So, it may be that the best engine of all is a Honda made in Japan, if you could get one. An old Briggs made in the US, if you got a good one or overhauled one that was undamaged, may be the second-best engine.
What I think all this comes down to, is if you value quality and reliability rather than originality, you might do well to go looking for a Japanese-made Honda, either new or lightly-used. If you value originality, you might go looking for an old Briggs of the same model SB used originally, which would be an 80102 I think.