Gigbags fit in the overheads. Didn't think they did till my last flight about a month ago. Only thing ya gotta do is make sure you're one of the first to board the plane. If they won't let you board after first class, and you can't find a free overhead they can store it in a closet (what we used to do up till last time), BUT you run the risk that there's no room. I called the airline to ask them to be specific with me about this "if there was no room" thing, and was told I wouldn't be able to get on the plane with it.

I've heard it happens, but of all my and my friends experiences (dozens), I've never seen it.
I've traveled also using just a standard hardshell case, and it's been fine. I just taped the case with duct tape to make sure it didn't open. People say they'll tell you to take the tape off, but that hasn't been my experience - and I live in NY. Travelled internationally also. Actually, ONE time they did make me open it but only because for some dumb reason the lady at check in though I said I was checking a "rifle" when I said "guitar". I could understand as they both sound so similar.
All in all, I don't think you'll have a problem either way.