Comment by bluGill

Some MUAs are pretty slow. It isn't hard to do better than a few of the MUAs I've used, and webmail often is better just because more people use them so more optimization has gone into them. I think this is the main one.

Webmail often has a really fast pipe to the email storage, which means it can get the headers faster and then extract only the parts it needs. Webmail is not required to use IMAP (though many do) an optimized protocol can offer advantages.