I use them both -- the BIS-push option is good for getting all your regular Inbox email and replying to that, so no need to start the GMail app. Where the app is good is when you need access to your gmail contacts (which may not be on your BB device) and when you need to access your labels. I have classes of email that's automatically filtered to labels and skips my Inbox, so it never pushes to my BB over the BIS connection; I have to fire up the app and open those labels specifically (which is what I want to do).
The things I filter out from my Inbox are topic replies to the bajillion forums I visit, shipping notifies from UPS/FedEx, etc. -- nonpersonal junk that doesn't really need my attention right away on my device. When I have a free moment I'll fire up the GMail app and go look at those sometimes, or they can wait until I get to a desktop PC.
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