I started out with just a pump, but I almost always just use the wick now. Works on big blobs too, it just uses up the wick faster. If you just want to stick with one method, I prefer the wick. I find it very tough to get all the solder and actually break a bond with just the pump. E.g, it would be almost impossible for me to desolder an 8-pin IC with a pump.
I started out with a pump first too, but they aren't the best. Like Al said, pump for the big globs, wick for the small stuff. Wick is great at getting solder out of plated-through holes when you need to replace a component. I've been replacing blown FETs on cards at work, and theres no way I'd be able to get a new part in the holes without using wick first.