For a small mailing (~50,000 total), exim actually beat out the other 2, sending 16/sec. to postfix's 15/sec. and sendmail's 12/sec. For a larger mailing, though (~250,000), sendmail raced to the lead, averaging 14/sec. to postfix's 4/sec. and exim's 8/sec.
So far, the results have been frustratingly inconclusive. We've definitely managed to improve things overall (I think we're averaging about 3x the average sending rate as when I first posted) but have seen no real consistency - things are better now but there's no clear winner between the three. Sendmail seems to have the edge for the larger mailings, as it not only can send quickly but can maintain the fast pace even as it delivers more and more mails, whereas the other two slowed down the more mails that we sent - which will probably get it the victory in the end - but all three mail servers are quite fast, and for the smaller mailings exim is actually, surprisingly, the fastest of the bunch.
I think by next week we'll have to make a decision, and unless exim or postfix trounces sendmail after a few more days of tuning and letting them run, I think sendmail will be declared the overall winner. (In the end, if the mailservers are sending over a million emails a day, the ability to maintain a consistently fast rate even under heavy load is the most important consideration, and currently sendmail's got the lead there.)
Oh, and for those curious, the best overall fs/mount options (of those we tested) is ext2 w/noatime. ext3 w/data=journal and noatime is a close second.