I have used both services for a few years each. They both work really well and make life MUCH easier!
Benefits of MobileMe
-Costs money but gives 20 GB of storage through iDisk
-Syncs bookmarks across computers and iOS devices
-Sync'ing of passwords, dock items and all personalized settings of computers
Benefits of Google
-Works better on Windows PC's, can use me.com on Windows machine but not as quick to respond as Google
-Flexibility of platforms (Android and iOS... MobileMe will only work on iOS)
My complaints with Google are that you cannot get access to bookmarks from an iOS device. This makes me sad, I love having my bookmarks everywhere. I use Xmarks to sync bookmarks now and use the Xmarks website to access those bookmarks. The app requires a premium subscription to Xmarks for use.
You can use Dropbox (2 GB free) instead of iDisk (20 GB, part of subscription to MobileMe). It's a fantastic piece of software!
Another thing to note, the Google services for email/calendar/contact sync'ing does not work as well as MobileMe through iOS and Mac dedicated apps (Mail, Contacts, iCal for Mac and the counterparts for iOS). You cannot get all of your google calendars to show up on iOS, contact syncing sometimes has conflicts (I have had 0 trouble with either of these things when using MobileMe). It's kind of a duh! though, MobileMe is made by Apple so it better work flawlessly on their apps.
Now take into account this is just from my experience (4 years now). Others may have negative feelings about one/both of the services.