If your mu4e is backed by a maildir on disk then it's pretty much assured to be slower than gmail or fastmail. One disk seek is very very expensive, and for many people a round trip to gmail's frontends is going to be faster. Gmail's speed will remain constant no matter how busy your local disk is. If you're compiling firefox on the same single disk that stores your mail, mu4e is going to take multiple seconds just to go to the next thread.
On the other hand if you have a good SSD then a local MUA running from local storage can look competitive.
On the other hand if you have a good SSD then a local MUA running from local storage can look competitive.