Along with absolute velocity I'd look at the rate of change in velocity as well as compare the actual velocity with the velocity you expect.
Rate of change - if the elevator is at rest and the cable breaks you can either wait until the car is going faster than it should to apply the brakes or you can, by the rate of change in velocity, predict that it will soon be going faster and apply the brakes sooner - for a safer stop.
Comparison - if your controls tell the elevator to be going up and you know it should go up at 0.5 meters/second then you ought to measure that value within a reasonable window. If you don't for whatever reason you could go into emergency mode - apply brakes, shut down. All you'll know is that something isn't right. Depending on the failure mode, you might actually "see" this sooner than the rate of change.
I'd do both if I could. Consideration for false triggering should be given. All of this would seem quite manageable with a capable controller.