I've done soldering for ~40 years, and learned from some excellent technicians. Many of them used solder wick, but my experience has been that unless the board is very high quality with thick traces, it's possible to wreck one very quickly with wick. Where I worked, most boards were MIL quality G10 stuff and it was easy - I did a fair amount myself. On consumer stuff, not so much; it's hard to find good wick (and I've tried expensive stuff) small enough that you can heat it along with the solder. The hotter the iron the more likely you'll lift the pad before the wick heats up. I found that a manual solder sucker (yes, a Soldapullt) works pretty well if you have small pads and a hot iron (and can get the honking great thing in there), but you have to position it very carefully to get the vacuum seal right on the solder while it's still molten or else you have to add more solder and try again. Since switching to a desoldering station my results have been 2-3x as good, and I haven't lifted a pad in a long time. All the heat goes right to the pad and lead, and there's no delay while you remove the iron and position the sucker. There's nothing like it for a big ground area or through-hole ICs.
So it strongly depends what you're working on, the quality of the board and assembly, and the tool. No doubt it can be done via any of the methods, but you should stick with the one which works best for you.