I use both and I prefer Analytics. It provides more information. They are not competitor products. They are complimentary tools.
Webmaster tools is what you want to use for getting an accurate picture of what Google thinks of your site from a content, links, and anchor text point of view. It can help you see where your SEO efforts are best spent. Analytics tells you where your traffic is coming from and how people use your website. It will help you track what hits are making you money and which ones don't.
There are two different thing, and both of them are important. By the way, if you ask which is more useful for me, i will vote for google analytic
Both are good tools with their own distinct purpose and come in very handy if used correctly. If you are trying to ascertain which one out of the two is more popular, it is definitely Analytics. Regards, RightMan
Both. Analytics is probably the more useful tool to track what is going on with your site as far as traffic goes. Webmaster tools will tell you if you are having problems with your site.