Your problem doesn't have (almost) anything to do with the CPU.
Transferring big files is usually fast, since it can be done with sequential I/O.
Transferring lots of small files requires tons of horsepower on the storage side of things, since it requires random I/O. Low seek times, fast hard drives, lots of cache and a filesystem designed for huge number of files are a must. CPU does not help there, at least not much, just like you are observing. CPU's and OS are just waiting for disk I/O to finish.
All that faster CPU / more cores can do, that they can end up waiting for I/O faster. :-)