It would be worth finding a late 50's or 60's Briggs (you haven't said what year your model B is) in the sense that it would be as close to original as possible. The challenge will be finding a 3hp Briggs with the stamped B&S pullstarter/blower housing with the right dimensions of the shaft for you to fit your clutch onto. Someone on here may have that engine. Try the wanted section.
The 5hp Tecumseh may offer some more satisfying performance however. There is no reason you or a another decent small engine mechanic couldn't get the existing Tecumseh engine running unless there is something utterly FUBAR with it...like a hole in the block or something majorly serious. Get a chinese carb, (or shell out the $$ for an OEM one), replace the fuel lines and air filter. Especially Don't screw with the tecumseh magneto unless you have a dial gauge or really know what you're doing. The small engines of yesteryear were made to be repaired over and over and not disposed of.