Try getting an IMAP PUSH on iOS or staying logged in to XMPP or SSH all day and you'll take that back pretty damn quick. How about not wanting to use their phone app and use SIP instead?
These are things I find necessary for day-to-day stuff, but which are simply impossible on iOS. If you want good 3rd party integration, Android is your only option in many cases. You just have to find the good apps.