In theory, a good optimizing compiler can avoid some of the stack manipulation necessary for naïve C function calls. (Obviously for those externally visible symbols where you must adhere to a platform ABI, you can't get away with this.) Even better, because the C stack isn't heap allocated, you can avoid malloc/free pairs for stack allocated values.

You get at least two drawbacks from this. First, your calling conventions are going to end up looking a lot like C's calling conventions, so you have to go through wild contortions for things like exception handling, tail call optimizations, green threads, and continuations. Second, you're subject to the limitations of the C calling conventions, so maximum stack depth (see recursion and corecursion), thread stack limits, and the safety of extension code written with access to the C stack are concerns.

You have to be a lot more clever to write optimizable code using the heap, but you get a lot of features from avoiding the C stack. To go really fast, you have to avoid copying a lot of memory around anyway, so my preference is to figure out how to optimize heap calls to avoid allocating and freeing unnecessary memory and to put everything into processor registers and keep it there.