without a doubt... use the plywood back.  ditto everything lucasjw already wrote.

I recommend using a plywood backing, then mounting the cabinets onto the drywall. This will create much sturdier cabinets to begin with, plus plywood is less likely to warp over time compared to drywall. This can be especially true in a laundry room if it gets warm and humid in there like mine does. Using plywood backing will also allow you more flexibility for anchoring the cabinets into a stud, while just attaching a backless cabinet to the wall makes this much more difficult. And down the road, if you (or a future owner) ever decides to remove/replace the cabinets, the plywood backing will leave the wall in better condition than mounting directly to drywall. Good luck and have fun!