I think the difference is in the tone they bring to your game. I prefer not to have psionics in a game with magic, and vice versa.
Actually, if at all possible, I'd like to keep psionics, arcane magic and divine magic entirely separate. A game with only divine magic is suddenly very different from a game with arcane magic, and a game with psionics if different still.
Actually, if at all possible, I'd like to keep psionics, arcane magic and divine magic entirely separate. A game with only divine magic is suddenly very different from a game with arcane magic, and a game with psionics if different still.