When matching 3-wire pumps to control boxes, you will probably find that a 3-wire pump of one brand will work with the Franklin 3-wire control box if the motor and box are specified for the same horsepower. Many but not all brands use the Franklin motor, in which case it would certainly work.
Now the question of buying a pump by simply matching horsepower is a totally different story. A 3/4 horsepower motor could be attached to a pump that would produce 5 GPM at 160 psi, or to a pump that would produce 20 GPM at 50 psi, or anything in between.
The "big box" stores and hardware stores usually stock one pump at each horsepower that provides at least as much pressure as most users will need. There is probably a 50% chance that you will get the right pump for your needs, and a 50% chance that you won't get what you need.
You need to get the information that shows the pressure and flow for the pump, and examine that to see if it meets your needs. That depends on the pressure at which you want to operate your system, depth to water in the well when pumping in the dry season, and the size of pipes and pressure losses in the system.
If you get the pressure/flow/depth-to-water data on the new candidate pump, and your existing pump, and characteristics of the well, someone here can probably help you avoid an expensive mistake.