Tough call. I like the board game concept of Mario Party and I'd say I love the earlier Mario Party games more than I love any Mario Kart games. That said, I tend to get my butt handed to me in Mario Party, whereas in Mario Kart I can at least be competitive with my friends.
If I had to pick one, I guess right now I'd have to pick Mario Kart just because I can actually put up a decent fight in it. If I were a bit more skilled or if my friends were worse and we were more even, and if the Mario Party games didn't suffer a downslide in quality over the years like Trundle mentioned, then it would have been Mario Party.