It depends not only on the brand but on the model. Most of us are familiar with the L-head B&S engines that have lasted so long in the past. Those engines are still substantial, but I have noticed nylon parts being used for the oil slinger and starter ring on the flywheel. I believe B&S is beginning to cut corners. Internal engine parts for B&S have traditionally been made of very good metal, but I've been seeing more component failure over the last few years, even from the L-head engines.
The B&S Twin (opposing cylinders) runs very well for a few hundred hours. Then the valve seats loosen and the engine will quit running after it heats up. For me, the V engines from B&S are not worth buying. Even though they have some pressure lubrication and filter, there are two many other problems from electrical to fuel pump.
The Kohler Magnum engine (all cast block) were arguably the best small equipment engine ever made. The Kohler command series, however, is not nearly the engine of the Magnum series. It is cast aluminum with cast iron bore and has oil pressure and filter lube, but won't last near the time a Magnum series would.
Parts are more expensive for the Kohler, too.
With all that said, and realize I have worked on a lot of lawn tractor engines, if you can only choose between B&S and Kohler, I'd go with the Kohler is the price is comparable. That's considering the recent products both have made.
Hope that helps!