Analytics is really great for checking how many visitors you get daily, weekly, monthly etc. It really does so much....You can find out were your visitors are coming from, it will tell you the bounce rate on your landing page (how many people clicked on then hit the back button) it tells you which pages are the most visited and how long people stayed on your site for. You can also create e-mail alerts for various things too. If you are running a PPC campaign you need to use analytics alongside it in order to track your results and make changes.
Pros - you can see more AdWords data imported in Analytics (Clicks tab). Cons - none at the moment If you are running AdWords campaign, you should really link them.
Another great advantage is, you can even see the position of your ad being clicked on. If you add e-commerce tracking for e-commerce site, it gives you an idea which ad position generates higher conversion.