In general, utf8_general_ci is faster than utf8_unicode_ci, but less correct.
Here is the difference:
For any Unicode character set, operations performed using the _general_ci collation are faster than those for the _unicode_ci collation. For example, comparisons for the utf8_general_ci collation are faster, but slightly less correct, than comparisons for utf8_unicode_ci. The reason for this is that utf8_unicode_ci supports mappings such as expansions; that is, when one character compares as equal to combinations of other characters. For example, in German and some other languages “ß” is equal to “ss”. utf8_unicode_ci also supports contractions and ignorable characters. utf8_general_ci is a legacy collation that does not support expansions, contractions, or ignorable characters. It can make only one-to-one comparisons between characters.
Quoted from:
http://dev.mysql.com/doc/refman/5.0/en/charset-unicode-sets.html
Both utf8_general_ci and utf8_unicode_ci perform case-insensitive comparison. In constrast, utf8_bin is case-sensitive (among other differences), because it compares the binary values of the characters.