Nine ball (9 Ball) is generally accepted as the more difficult game of the two, simply because there will never be more than one object ball at a time. This clearly limits the player's shooting options, whereas in eight ball (8 Ball) the player can have many shots to consider at one time.
Additionally with nine ball, a your opponent can easily play safe if a run-out is imminent, making it very hard for you to finish your game.
On the other side of the coin, one could say that even though there are oftem many object balls to consider at one time in eight ball, players must deal with clustering of the balls. How many times have you seen a player practically run a table and then miss their last ball or two since there are too many of their opponent's balls remaining on the table. The opponent then comes back to win the game, since they have practically an open table to play.
That being said, I think you'll find that most billiard players will agree with me in that eight ball is more of a beginner's game. Others will maintain that the two can not be compared, as the games are simply to different in nature. You may also encounter a lot of bias in responses to this thread, since most players have a preference one way or anohter.