Phasers are more sophisticated
There's something to be said about the aesthetic of the blasters from Star Wars, but the truth is that the phasers of Star Trek are just a lot more useful. For one thing, they have a stun setting, meaning you can use them to apprehend someone without having to kill them. For another, they don't have that weird functionality where minor characters are instantly killed by a graze while heroes important to the story are simply tickled. Blasters are for killin', phasers are really an intergalactic multi-tool.