That's correct. BB acts like a combination of POP and IMAP, where there's a looser link between the mobile inbox and the server inbox. The iPhone tries to make everything act like IMAP, where what you see on the mobile device is the same as the server. Good for Enterprise actually works the same way.
On my Blackberry, search worked very well. On my iPhone, I can send an e-mail yesterday, and put in keywords from that e-mail into a search I conduct today, and it *won't* find the e-mail....even if I tell it to look on the server also.
iPhone mail search only searches to, from, and subject. It does not search body. That sort of sucks.
If I create an event on my calendar on my desktop, it gets pushed to my iPhone. Which is obviously important. But if I'm at a client's office, and I make a meeting with them on the spot, and book it on my iPhone calendar, it *doesn't* push over to my Google calendar.
I don't use a google calendar, I use iCloud (and formerly used MobileMe), and my entries do push to everything else I have. When I use Good for Enterprise, the same thing happens for my corporate outlook calendar.
It could be something as simple as the default calendar being set to a calendar that's only on your device, or there might be something in the way you have Google Calendar set up. There are several different ways to set up google calendar, and I'm not as familiar with the limitations of each. I'm reasonably certain there's a way to get it to work, but I'd definitely agree that Google's calendar works better with Google's apps. Are you using the calendar via Google's exchange setup or via caldav?
The final problem I have is how contact backups are done. After going through the default wizards with iOS, I have found that if I make a change to a contact directly on my handset, and later sync, and my backed up copy has older information on it, the older information actually replaces my corrected information on the phone.
How are you syncing your contacts, and what are you syncing them with? Are you syncing with your local Mac Addressbook via iTunes, with Google via its Exchange support, or some other setup?