In current Linux, I'm pretty sure both of them use the same underlying page cache. fread() adds a small amount of management overhead, but read() does just as much system level buffering. mmap() uses the same cache, but just gives direct access to it.
But it's possible I'm wrong, and I don't seem to be able to find a solid source for this online. This page references this, though:
I feel like I've read other more explicit descriptions, although possibly offline.
I don't follow the rest of your caching arguments, though. read(2) exploits the buffer cache; in fact, the rap on mmap() is that it makes worse use of the buffer cache, because it doesn't provide the kernel with enough information to read ahead. Apocryphal, though.
The big issue is that the mmap() case is much more demanding on the VM system. You're thinking only of the buffer cache when you talk about caching, but the X86 is also at pains to cache the page directory hierarchy (that's what the TLB is doing). Hopping all over your process' address space rips up the TLB, which is expensive. There are also hardware cycle penalties for dicking with page table entries.