I’ve tried it out on MySQL 8.0.13 and compared LIKE vs REGEXP on a table with 1M+ rows on a column with an index:
SELECT * FROM table WHERE column LIKE '%foobar%';
Query took 10.0418 seconds.
SELECT * FROM table WHERE REGEXP_LIKE(column, 'foobar');
Query took 11.0742 seconds.
LIKE performance is faster. If you can get away with using it instead of REGEXP, do it.