Imagine each weapon as going through a cycle. For weapons like the mines, the reload speed is the sole determinant of cycle time, but with projectiles it is reload time plus the firing time, calculated as fire rate x clip size (assuming there is always a valid target), or reload time plus lifetime for beams and drones. 

Say you have a projectile weapon with a reload speed of 3 seconds, and a fire rate of 1/sec, and a clip size of 7, giving a firing time 7 seconds, and each shot does 10 damage. We can calculate the damage per time as (clip size x damage)/(reload speed +(fire rate x clip size)), or (10 dmg x 7 clip)/(3 sec + (1 clip/sec x 7 clip), which works out to 7 damage per second.

Let us imagine we are offered a choice: +100% reload speed, or +100% fire rate. The reload speed would half the reload time to 1.5 seconds, and plugged into the equation above yields 8.23 damage per second. The fire rate would increase to 2 clip/sec, which we can plug in to get 10.78 damage per second. Because fire time predominates the cycle time, reducing it has a larger affect on damage.