They're completely synonymous. Use whichever one you prefer.

Hi Hunter, 'Outwit' and 'outsmart' mean about the same thing... but, according to the Corpus of Contemporary American English (COCA), 'outsmart' is used more often than 'outwit'. Generally, in North American English, 'smart' is used more often than 'wit'... 'smart' is a pretty everyday word that can be used in lots of ways. 'Wit' is more specific and so used less frequently. The upshot is probably this: 'outsmart' is more common generally, it's definitely more common in speech, and it's probably the default choice. Use 'outwit' to upgrade your level of formality or to be more specific. I hope this helps!