Does paint adhere better if sprayed on or brushed on?

It will depend much more on how well you prepare the surface. For file cabinets with a factory paint finish, sand them evenly with a very fine grit sand paper, like 300 - 400, and then wipe with acetone if the paint will be oil base. Wipe with warm water if the paint is going to be water based. If it was me, I'd spray them because I don't want the brush strokes.

sand them lightly to get a rough surface (better for the paint to stick to), then paint them. Spray works well, better for large surfaces (and faster too).

Consider that spray paint is used almost exclusively in all industry.

Its gonna stick the same either way. The main difference is that if you spray you will generally get a smoother finished product without the brush lines. Id prime it first and then go to town.

As long as you prep the surface first, it don't matter.