Note: Since MySQL 5.5.3 you should use utf8mb4 rather than utf8. They both refer to the UTF-8 encoding, but the older utf8 had a MySQL-specific limitation preventing use of characters numbered above 0xFFFD.
utf8mb4_unicode_ci is based on the Unicode standard for sorting and comparison, which sorts accurately in a very wide range of languages.
utf8mb4_general_ci fails to implement all of the Unicode sorting rules, which will result in undesirable sorting in some situations, such as when using particular languages or characters.
utf8mb4_general_ci is faster at comparisons and sorting, because it takes a bunch of performance-related shortcuts.
On modern servers, this performance boost will be all but negligible. It was devised in a time when servers had a tiny fraction of the CPU performance of today’s computers.
utf8mb4_unicode_ci, which uses the Unicode rules for sorting and comparison, employs a fairly complex algorithm for correct sorting in a wide range of languages and when using a wide range of special characters. These rules need to take into account language-specific conventions; not everybody sorts their characters in what we would call ‘alphabetical order’.