Google webmaster tool and Backlinkwatch both have their own techniques. GWT also shows the Nofollow links. GWT will show some backlinks. Yahoo site explorer will show all the back links.
Depends on what you want to do. If you are optimising your site GWT is more accurate and gives you details about your site that other tools can't. If your doing competative analysis than GWT wont give you the information you need so tools like Backlink Watcher, Traffic Travis, SEM Rush, etc should be used in combination instead. Personally I dont think one tool is better than another. They are all useful and serve different purposes.
Majesticseo.com blows either one of them away. 7500 link limit instead of 1000, showa backlinks over time from multiple sources, the ability to overlay your site with your competition's. Priceless...
What is this Backlink Watcher you speak of? I searched and couldnt' find it. I've been looking for a tool for that lately. As far as GWT, it seems to be really slow for me, links not showing up as quickly.