I can recall three games that I played the home versions of before playing the arcade versions -- Legendary Wings, Rygar and Trojan. The NES versions of these were three of my favorite games growing up, and at the time I wasn't even aware that arcade versions existed!

I ran into the arcade version of Rygar a couple of years after playing it on the NES, but in the case of Legendary Wings, I didn't see this one in the arcade until the mid 1990s. Even now, I still like the NES versions of both of these games more (especially Rygar -- I've never liked the arcade version of the game). The arcade versions were definitely nicer looking, but I was accustomed to how the NES versions played, so I preferred them, and still do even today. As for Trojan, I've never seen it in an actual arcade; my experience with the arcade version has been solely through MAME.