The difference between 15 or 16 gauge nails is not significant. The nails secure the panels in place while the glue dries. Cabinets are strong because they are fitted using joinery and glue, the nails are almost incidental.

I have built and am currently building cabinets for my home. I use an 18ga nailgun and a 1/4" staple nailer for attaching the thinner plywood backs. TomH is right on the money about the gule and joinery. That is what gives strenght to the completed cabinet not the few nails to hold it together during assembly. I'd rather not have to deal with lots of nail holes to be filled during finishing. Proper Joints, glue and clamps!