With concrete, if you're worried about strength and stability, the solution is to simply lay a thicker slab on concrete. Because of this, contractors laying concrete rarely worry about preparing the base. The ground underneath a concrete driveway may be prone to shifting or sinking, and there's really no way of knowing what's down there until it's dug up.
Laying bricks over concrete creates two worries:
1. The unprepared sub base
2. The concrete itself
If something is wrong with either of these layers, it will show through the bricks. Unfortunately, when brick driveways are done over concrete it could be resting on an unstable base, the resulting bricks will be prone to instability. Expansion joints in the concrete will quickly turn into cracks, which will require costly repair jobs. In extreme cases, shifts in the ground could crack the entire surface, just as a house's foundation may crack if improperly laid.
So putting brick pavers over concrete may seem a lot easier, less costly and look good at first, but there are bound to be problems over time. It just doesn't make fiscal sense to do it, as that driveway will need a lot more work in the near future. So in our opinion it is best to remove the concrete first.