The cost will probably be less for painting but not much. Both require a lot of surface prep. Painting would require some sanding, repairing of any issues, cleaning off anything that would prevent paint adhesion, primer and at least 2 coats of paint.
Staining will require more prep work. You would need to strip or totally sand the existing finish from the cabinets, fix any issues, stain and put a top coat of your choice on. The top coat might take 3 or 4 coats to get a good durable finish. If you don't remove the existing "factory" finish, you stand a very good chance of getting a blotchy stain job because you're not starting with a surface that is all the same color and of the ability to absorb stain.
We opted to paint.