Summary: We think you have short pull brake levers. Short pull levers work on either road brake calipers or cantilever brake calipers. Long pull levers were introduced to work with linear pull brakes (v-brakes) which require more cable pull. Long-pull is the norm for off-road these days. So your levers should work with mechanical disc brakes meant for road. BB7 has a road version, and Spyre is a road version. Spyke is the long-pull version of Spyre.
BB7 is a single-actuator caliper; and it only moves the outer pad. It works by deflecting the rotor into the inner pad. Proper adjustment involves adjusting the inner pad as close to the rotor as you can get without rubbing. That's an adjustment that Spyke/Spyre don't need. Both will stop you fine, but BB7 will be a little 'fiddy-er'.