In my experience, both pump solder suckers and solder wicks are effective tools to remove solder. However, there are specific situations where one works better than the other. For example, the suckers will remove solder faster when working on through-hole parts (once the solder around the lead is molten), but when dealing with SMD pads using wicks is the faster method.
Oh and funkyguy4000, all the solder suckers I've used have had at least one way to get the collected solder out of the sucker. It looks like the design Doc linked to in the original post is the type where you can unscrew part of the lower cylinder to remove the old solder.