I had to correct your spelling there: πεις, not πες.
In the context you’ve given, both are subjunctives, following μη “don’t”. Λες is the present subjunctive, meaning it’s imperfective (continuous); πεις is the aorist subjunctive (perfective). So “don’t keep telling me” vs “don’t tell me” (once-off).
Why would the lyricist switch aspect in the verb? Variety: he gets to say the same thing in the chorus twice, but with a different rhyme:
Μεγάλα λόγια μη μου λες
όσα ακούω τα ξανάκουσα τόσες φορές
Μεγάλα λόγια μη μου πεις
μείνε και τίποτα μη μου υποσχεθείς
Don’t keep telling me big words.
What I’m hearing I’ve heard so many times before.
Don’t tell me big words.
Stay and promise me nothing.