10
Full-text search is the kind of search based on special sort of index (full-text, obviously). So you get the power of O(lgN) while searching using it.
While like %% always causes table fullscan which can be terrible slow (when you have 100k and more rows).
Personally I use Like %% when it is a small table (0-1000 rows) and I'm sure that it will never grow (and, important, when like %% fits the task requirements).
Note: fulltext indexes are available only for myisam SE. If you use innodb - then you need to look at some 3rd party indexing software like sphinx