This is an interesting one. Which control method you want actually kinda depends on what weapons and ships you use.

If you're planning to go with a fighter or grappler relying on swift movement, changing of direction, and short-range abilities, often ALL AT THE SAME TIME, the gamepad is definitely a better choice if you know how to use it.
However, if you're a fan of the railgun or the gemini laser, go for the mouse controls, like me.

And for the third- and second-to-last mission in the campaign, you'll want a Gamepad unless you can cope with your cursor suddenly having mass. Not ideal.

So yeah. If you play at range at need aiming, M/KB. If you play up close, need to turn fast but have weapons that aren't as easy to miss with (Grappler Cone abilities qualify), then go for Controller.

M+KB > Gamepad
Accuracy in both long range shots and directional correction just have me playing at a higher skill level. I'd also recommend rebinding some of your keys for better ergonomics.

HOWEVER,
Gamepad feels VERY different and is a fun experience as well, just drop your difficulty a bit to compensate.