The Touch Diamond 2 runs on Windows Mobile so you can pretty much install whatever apps you need to run. It also has everything you would expect of windows e.g a proper mail client, mobile version of the MS Office apps etc and a mobile version of MSN messenger.
The G1 is a HTC device too but it runs on the Android platform which IIRC is an open-source (think Linux) platform developed in conjunction with Google. As Soulkiss mentioned, it is very geared towards Google e.g Gmail which has its issues. Not sure on availability of apps etc for it though, haven't used one myself.
If the internet browsing is your main priority, you can't beat the browsing experience on the iPhone IMO, but the other apps and the rest of the platform are very restricted compared to WinMo. I went with the TD2 as I've had WinMo devices for years and use lots of 3rd party stuff on them such as TomTom. You can 'jailbreak' the iPhone to allow 3rd party apps but it invalidates your warranty.
More info on all HTC devices including the G1 here:
http://www.xda-developers.com
Also
http://www.coolsmartphone.com for lots of device reviews and info, including iPhone / Windows phone comparisons.