What you are showing is an implementation without long macros. It is cleaner and simpler. However, it is slower as compilers often can't inline user-provided comparison functions (though modern compilers seem to do a better job). For integers, extra comparison function calls are costly. With tree.h, you can implement the comparison in a macro. Then compilers will automatically inline the comparison. That is the most efficient way to implement generic binary search trees.
I don't think this matters too much. It's the overhead of an added call/return that is hot in the cache and the CPU has enough cycles of twiddling its thumbs while it's grabbing the next tree level from a lower cache or main memory...
You are right. There are lots of more operations in addition to comparisons. Just done a microbenchmark. The difference between macro- and function-based comparisons is largely indistinguishable.
