Let me talk about the Mail at MobileMe first. This just came out of beta, (on the web) and the features they added are very nice. First off, I think the attempt is to make it look like the iPad app for Mail. It has three columns, the Mailboxes, the Inbox, and the message pane on the right. Kinda like the newer versions of Outlook, or maybe even Mail.app (if you have the three column view turned on).
At the top there there are buttons, from left to right, they have the "Cloud" Icon (which is basically the Application switcher, allowing you to go back and forth between Calendar and Contacts, etc), the Search pane, Trash, Archive, "Move to Folder" Reply (and reply to all, and forward) and "New". Over on the right you have the "gear" icon which is your "Preferences", and then your account manager (under your name over there).
Mostly everything works the same as the older MobileMe web app, or the same as you'd expect from any web-based Email GUI. One thing that they did add was "Server-side" email filtering. Now, it's still pretty limited as to the functionality, and I don't know if there are plans to expand this functionality, however, for me, it gets the job done.
MobileMe features "Push Email" to all your Apple devices, and what's nice about the server-side rule filtering is that emails that are filtered on the server are not pushed to your mobile device. Why do I like this? Because after I found this out, I switched all my listservers over to MobileMe and off of Gmail. I actually don't even use my Gmail account anymore. MobileMe, is a traditional IMAP server (no "labels are actually folders" or whateverness of Gmail. (Oh and that stupid "All Mail" folder. I hate that thing) It works. It works well, and it's fast. Gmail bandwidth throttles their connections via IMAP and POP, leading to much irritation. I use MobileMe because, once you get past my server side filters, (which are quite extensive), you get pushed to my Mobile device.
Could I do this with Gmail? Yes. Gmail does feature server-side filtering. Gmail does push email to the iPhone with the "Exchange" connector. However, not only for the above reasons, but for one stupidly simple reason in addition: When you reply to an email on Gmail, you don't get the reply icon in your Mail client. So, basically, you don't know which emails you've replied to, or not replied to until you log into Gmail on the web. Maybe this is the way they get you to log in and see their ads, but either way, it's stupid. So yes, I use MobileMe for all my email, aside from work.
So, what's new recently?
The Calendar just entered a new phase of beta. When MobileMe has something in beta, when you log into the web interface it will ask you "Do you want to try out the beta?" You click "Okay", and a couple of weeks later they make you eligible for the beta. I requested my invitation last week, and got it yesterday.
After I logged in, it asked me "Do you want to upgrade your calendars?" I clicked "Ok". This whole process took about 10 minutes. Upgrading my calendars and everything.
It not only changed the calendars on MobileMe (which, now look just like the iPad), with the ripped edges and what not.
But they also change your iCal calendars and your calendars on your iPhone into "Caldav". What does this mean for you?
Finally, (why did this take so long Apple? Nice job, but seriously?) you can send invites to other people on your Calendar on your iPhone. You can accept invites as well, just like the iPhone does with Exchange, if you receive a calendar invitation, you can accept or Deny it right on the iPhone or iPad with MobileMe. (This feature requires iOS 4, unless you manually add Caldav into your iPhone as a calendar)
You can share your calendar (see in the above screenshot where the "Home" Calendar has a Green button next to it? Indicating that it's shared? You can share it with individuals or the world. (It used to be "The World".) You can see the "Free-Busy" schedule for anyone on MobileMe (that's in the beta, but after it comes out of beta, it'll be normal.)
All in all, it looks great, and it works great. I've only found one bug (I'm in the beta, I'm supposed to report this stuff right?) it's an html5 rendering problem with Chrome (works fine in Safari -- surprise!). You even have a nice "To-Do" bar on the right. Now, only if we could get a "To-Do" feature on the iPhone, I could do away with these wonky third party apps to manage that stuff.