I've found that sometimes both works. Especially for through holes, the de-solder braid may not get in deep enough on the PCB hole to suck up all of the solder,

I've found that sometimes both works. Especially for through holes, the de-solder braid may not get in deep enough on the PCB hole to suck up all of the solder, and repeatedly heating up the same area on a PCB is a bad idea. Heat it up, swift downward motion (slamming your fist on the table holding the PCB between your finger and your thumb) and the solder will come flying right out.