I think
DracoDragon42 and
Mistery Meat nailed a great detail on their edits, by making them a little bit more messy, and you started taking that path with your last edit too.
Having that in mind I did my own attempt at it.
An energy beam (wich is how I interpreted your beams as) would probably be less "controled" and "mechanical" and look more like plasma. So I would suggest you going for more a more imperfect and organic look, with more jagged or doodly lines instead of laser-like straight lines. That would not only make it look more natural and readable, but more dynamic too.
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As you can see, even the clash of the beams is asymetric, and I added small sparks or particles flying everywhere to enhance that messy look even more. Think about how an explosion, with stuff flying everywhere, or paint splashing against an object would look like to get the idea.
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Then I just polished a little bit and added more colors. There is still a lot of room for improvement on it, but it shows the basic idea that comes to my mind when I think about two guys shooting beams at each other.