You might want to search thearchives since this has come up a couple of times, but it comes down to this. In terms of raw CPU speed, there is probably not a difference anymore. Both CPU technologies are essentially huge computers on a chip or a small set of chips. The differences lie mainly in reliability and I/O capabilities. Mainframes have a lot of redundency and servicability features built in. The way they handle I/O tends to be much more efficient than the 'lower end' boxes since they are able to handle many (hundreds? I don't know) of simultaneous I/Os. Also the S/390's means of doing paging I/O is very, very fast. And it depends on who you talk to, but in recent years, mainframes have been cheaper to operate than large farms of networked PCs when you factor in support costs (personel, infrastructure, backups, etc). The goal of decentralization has turned into a nightmare of cost and managment issues in some cases. 
 
I'd add that mainframe software (at least system software) tends to be written with the old ideas of efficiency in mind. Yes, it has gotten more bloated than it was, but it is nothing compared to the bloatware on PCs. You know, you install a little clock program on a PC these days and you see things like 8MB downloads. If someone in a mainframe environment shipped a dumb utility like that and it took up 8MB, even including doc, runtimes, source, and their mother's favorite fruitcake recipe, they'd be cast out into the land of the burger flippers. But that is a software issue, only related to your question in a more cultural sense.
 
A more interesting question is what is a mainframe. S/390 and its ilk, probably Alpha and similar high-speed multi-terrabyte capable data warehouses, but it basically comes down to I/O: how much and how fast.