This is probably my favorite tool for competitive analysis. It's called BuiltWith.com and it's basically a database of all web technologies. The same way google takes a snapshot of every websites content, BuiltWith takes a snapshot of every technology running on a website. The data this can uncover for you is amazing. You can see which tracking tools they use, which shopping cart, which email forms, which payment processing, which ad serving cookies, and so much more. You can often tell how sophisticated a competitor is just by looking at how advanced and up to date their web technologies are.

My personal favorite thing to check is which retargeting and programmatic advertising cookies they have on their site. This lets you see how they buy their media, and can help you find scale for your advertising efforts.

If you can't afford BuiltWith, you can also go ahead and check the page source code for your competitors home page and look at what code snippets are running on it. This wont give you as much insight, but you can usually see which cookies they are dropping and which analytics tools they are using.

Happy Hunting.