Steppers
Pro
Very simple electronics
Con
Very limited power
Quite limited torque at high speed
If they lose a step, that's it, and you may not be told about it unless your controller is quite expensive)
Servos
Pro
Much bigger range of power available (as much as you want)
Much higher speeds available with torque
If they fault (position error too big) they tell you
Con
Slightly more complex electronics and mechanics (ie encoder)
Higher cost typically
Controller needs tuning
As for brands - generally, You Get What You Pay For.
I use Gecko+servo, and cannot comment on other combos.
Cheers
Roger