I found a short thread discussing this change on the IronPython mailing list:

http://www.mail-archive.com/users@lists.ironpython.com/msg11...

It seems like a public image choice more than anything, even though "Microsoft Public License" was an OSI-approved license it still carries the dreaded M-word. Plus people are more familiar with the Apache license.

Someone in the thread also commented that Apache License 2.0 is designed to be GPLv3-compatible whereas MPL was less clear on GPL compatibility.