Do note that modern compilers can detect when the return value of the ++ operator is unused, and skip the extra steps when unneeded. (I've verified the resulting assembler myself from GCC 3.X.) That said, I still use the prefix notation because I can't come up with a good reason not to.
Neither one really has a direct "equivalent" in assembly.
Prefix is going to look something like:
inc eax # increment the value
mov eax,ecx # copy the return value to its destination
Postfix is going to look something like:
mov eax,ebx # copy original value
inc eax # increment value
mov ebx,ecx # copy original value to final destination
The actual code you'd get would vary a lot between compilers, architectures, and even just different contexts within the same compiler-architecture combination.
On the flipside, using pre-increment introduces a dependency, which means the processor can't do Out-of-order execution on instructions using that value...