The MySQL extension is very slightly faster than MySQLi in most benchmarks I’ve seen reported. The difference is so slight, however, that this should probably not be your criterion for deciding between the two.
Other factors dwarf the difference in performance between mysql and mysqli. Using mod_php or FastCGI, a bytecode cache like APC, or using data caching judiciously to reduce database hits, are far more beneficial for overall performance of PHP scripts than the choice of MySQL extension.
Don’t be penny wise and pound foolish! 🙂