I'd much rather have anime over CGI any day, but really, it depends on the game. When they remade Valkyrie Profile, I couldn't stand to buy it because they replaced the anime-ish cut scenes with CGI. They also blend very well with the higher quality cell shaded games like ZOE2. Another game that comes to mind that anime scenes were used to great effect was Tales of the Abyss.
Hell, I remember when it was an amazing thing to come across an anime scene at all in a game and it warranted a call to my friend to talk about it when one would crop up. Much the same for voices as well =P. I'm fairly certain that my first one was Thousand Arms(my first taste of dating sims as well =P) and The Granstream Saga.