Full Text Searching (using the CONTAINS) will be faster/more efficient than using LIKE with wildcarding. Full Text Searching (FTS) includes the ability to define Full Text Indexes, which FTS can use. I don’t know why you wouldn’t define a FTS index if you intended to use the functionality.
LIKE with wildcarding on the left side (IE: LIKE '%Search') can not use an index (assuming one exists for the column), guaranteeing a table scan. I haven’t tested & compared, but regex has the same pitfall. To clarify, LIKE '%Search' and LIKE '%Search%' can not use an index; LIKE 'Search%' can use an index.