I'm using Cairngorm with the UM extensions, not because I'm particularly fond of it, but because I work for UM and that's just what we use. Sometimes it seems to be a bit more work than it's worth, but for big multi-developer projects it's a great solution.
I listened to the Flex Show podcast talking about mate (there's a link on the mate page) about a week ago, and it sounds interesting but I haven't tried it out yet.
We have decided to go with Cairngorm mainly because of it seemed to be a bit more supported by the Flex community. However I did look at PureMVC and thought that it looked a bit more robust, also the ModelLocator singleton seemed a bit odd, but I have been able to get around it's quirks.