I can say MobileMe just introduced the mail rules which was always available on Gmail. Overall I enough Google mail over MobileMe. If you have Google Apps Premier, you can use Postini filtering which is even more robust.
In terms of sync, they offer similar sync services from contacts to calendars, with MobileMe offering their own preferences syncing on Macs and the Find My iPhone interface for finding your misplaced iPhone, iPad, or iPod touch. It makes initial setups a piece of cake. I have a family account (as the master) and it's easy to manage sub-accounts via the web control panel.
As a plus in the Google department, they have much wider integration support with devices; they can sync with Blackberry and Symbian devices; they have an Outlook plug-in for work; the do sync well with Apple Mail.
Overall, I enjoy both services and they suit my different needs; for home email I use MobileMe to synchronize my machines and devices. For my work, I use Google Apps Premier.