Student or Learner
Which is the right expression: " you owe me" or "you owe me one"?
***Neither a teacher nor a native speaker.***
I would choose:
You owe me one.
Usually you owe somebody something.
Leaving out the object makes it sound incomplete (to me), although it might be correct too.
As usual, context is everything!
If someone does you one favour, you might say immediately afterwards "That's great. I owe you one!"
If someone has been doing favours for you for a long period of time and you finally get the opportunity to do something nice for them, you might say "Let me pay for your lunch. After all, I owe you."