It is a VERY slight difference. In fact, they are so subtle that they are entirely interchangeable. But if you want a thorough clarification, I'll try my best:
"Just leave me" tends to focus the attention on the person walking away from you (physically) or breaking up with you (a separation). Saying "just leave me be" focuses the attention more on yourself, and you are asking someone to allow you to leave so you can focus your thoughts inward. Please let me know if I did not explain this well enough.