Of course, if we assume the colors represent something real rather than just artistic license, then you'd want to have blue beams rather than red, because blue light is higher in frequency and energy than red light. So a blue beam would be hotter and more powerful than a red one.
However, that clashes with our psychological expectations; we see red as a "hot" color because we associate it with fire, and blue as a "cool" color because we associate it with water. So FX artists tend to get it backward, using red beams to connote higher power than blue beams. (Case in point: in the '09 film, the hand phaser's beam is red on kill, blue on stun.)
Although come to think of it, maybe a red beam would be better. If a beam is radiating light out to the sides, then that represents energy that's being wasted and not delivered to the target. So maybe a red-glowing beam isn't necessarily more powerful, but more efficient, wasting less of its energy. But no, I think that's a reach. If the beam is high in energy, its waste photons would be as well. If it were more efficient, it would just lose fewer photons in the first place; it would be dimmer, not redder. At least, that's my instinct.
This is why, ideally, you want an invisible beam. Not only does it waste a minimum of energy, but hey, it's harder for the enemy to track back to your firing position. Always a plus. (Which is also why brilliant glowing torpedoes are a silly idea, more a conceit for the benefit of the audience than something that actually makes sense in-universe.)
