I have noticed a couple of things that work differently since I installed ios6 on my iphone4. First of all, I did a complete fresh install/restore. I too like the look of the new decline/accept/maybe buttons but find they don't always seem to respond. My primary beef however, is that it used to be that when you accepted (or any action for that matter) the email with the invitation would move to the deleted items folder, as it does in Exchange. This issue has nothing to do with Google sync, as I am not using that. I use standard Exchange (Active Sync).
I have had other issues that I cannot recall accurately enough to report at the moment but they definitely have to do with sometimes finding that I have to accept the invitation on my iPhone and then again in Outlook on my PC.
Almost all the invitations I get are sent from Exchange (either from a PC or a Blackberry user going through The Blackberry Server. I also get some from my wife's iPad. I will try to make a note of the source when I observe these different behaviors as I hadn't considered that to have been a possible cause.
Either way, it doesn't work as efficiently as it did in ios 5.x