I tend to like board games more because of the visual aspect. The ones they make now with all the mazes and stuff make it more exciting, but then again cards are easier to deal with since everyone doesn't have to be hurled together to get to the board.
I like card games best because if you have a deck of cards there are dozens of games you can choose. And you can play everything from solitaire to multiple player games. Second, would be paper games. I like games where you have to think and use your mind. Solving puzzles is a challenge I love. Third, is board games. They are a lot of fun with the right people. Dice games come in 4th. They usually are more games of chance than skill. Though they can be fun in the right circumstances.
I was going to say "board" but then I really like RPGs which require "paper", so paper wins. Besides that I love the look and feel of a board game.