The difference in price may be because of it being either ½" or ¾". In determining what plywood to use would depend on what you want it to look like and how the particular material will fit in with the surroundings.
The other consideration is whether to make them frameless or face framed. A face frame would add some strength to the cabinet, but if the sizes are not excessively large, a face frame isn't a must. A frameless cabinet is easier to clean, offers more open accessible space, enables the use of cabinet wall hinge plates, and doesn't require all the material and labor to make and install frames. Drawer hardware works out better. I might use a face frame if it had to match other cabinets, or if the face frame was an integral design feature for the cabinet. In some cases doors may be desired to be inset (flush) with a full face frame showing. Or some ornamental design may be incorporated to the frames' faces.
Your materials choice may not have to be plywood. It may depend on how the exterior of the cabinet will be finished. For a utility cabinet, or one that needs to have a woodgrain or laminate exterior, a melamine cabinet might be a good choice. It needs no interior finishing, is durable, and easy to clean. The exterior can be veneered or laminated with a Formica type laminate, or, ¼" hardwood plywood could be used as a veneer.
If your materials choice will be a plywood, independent hardwood plywood distributors usually carry a better selection of sheet goods. Domestic grading for plywoods vary from what you'll find at the box stores. Some plywood veneer faces don't finish well, like some of the Sandply's, Meranti's, Luan, or any of the Virolas. They just won't look like a distinctive hardwood veneer. Faces like Birch, Maple, Oak, can be finished to look very good. If you have to purchase plywoods, no matter where, check out the sheets completely. Some defects will be hard to find. Check for any delamination on the edges, any differential in the sounds to the face veneers by tapping, or variations in the integrity in the veneers...high/low spots.
Birch or Maple would be a good choice for cabinet boxes. Of course for utility or shop cabinets, you could use MDF, or even particleboard. Fabricating with sheet goods IMO works out best using dadoes, rabbets, glue, and fasteners if applicable. I wouldn't use pocket screws or biscuits.