There’s a slight register colouring in κοίταγε: for -αω verbs, Standard Modern Greek exceptionally uses a Northern Greek imperfect ending, -ουσ-, whereas Peloponnesian (on which Standard Modern Greek is based) uses -αγ-. This means that κοίταγε sounds more informal than κοιτούσε, whereas κοίταζε is unmarked.
In practice: none. κοιτάω and κοιτάζω both mean “to look”, and are just morphological variants—of a kind quite common in Middle Greek, as new present tenses were being reconstructed from aorists. (Both -αζω and -αω verbs could have -ασ- aorists; so working backwards, you could end up with either present tense.)