Probably the most annoying thing currently about using applications on more than one platform: notifications not syncing.
By the end of a workday my phone is full of push notifications and app badges I have already dealt with using the computer. As a result I find myself regularly doing rounds of cleanup: opening up apps one after an other to have them clear the badges. It’s partly because I’m obsessive that way and also because notifications kind of lose their meaning if read ones are not cleared.
I do like badges on app icons in iOS, don’t get me wrong. I missed them a lot during my few months of being an Android user. For me they work like a to do list: I can see which applications need attention. I only wish they would sync, like if I read a Facebook comment on the computer then the iOS app would lose its badge too, and the relevant entry in the Notification Center would disappear as well.
This is the aspect in which iMessage currently beats every other service: not only do messages arrive on all connected devices but the notifications are also constantly kept in sync and being removed when a message is read on another device.