If cable pull is similar enough, it will work. If lever is pulling more cable than the caliper needs, feel will be firm, but stopping power will suffer (slightly, unless cable pull is waaay off). Vice-versa, if lever pulls less cable than the caliper needs, feel will be squishier, but stopping power will increase. Best is to get it spot on.

Also, good clean rims, good brake pads and well set up calipers play a role in stopping power.

Wrote in detail about brake compatibility here:
8) Compatibility - mechanical bicycle brakes - Cycle Gremlin