Both terms have their uses. While "Become a Fan" would be ideal for personal pages of celebrities, movies, brands, games, etc, I don't find that term ideal for businesses, or statements, reviews and some such, where "Like" would be far more appropriate.
Both terms have their uses. While "Become a Fan" would be ideal for personal pages of celebrities, movies, brands, games, etc, I don't find that term ideal for businesses, or statements, reviews and some such, where "Like" would be far more appropriate.