You can use Google Analytics, as well as, Quantcast. However, the one complaint I have with analytics is that sometimes it tends to hang your page. This actually can be a pretty big turn off to a new visitor as you've literally got 7 - 10 seconds to catch their attention before they decide to close your page. So if your website hangs, they won't think twice about it and move on to the next site.
An Alexa ranking that gets lower means your site is getting better, the higher the Alexa Ranking the less visitors your site is getting, can get easily confusing for many
Analytics is a traffic measurement tool for your site. It's not to spy on your competitors. The data you can get from Analytics will allow you to improve in many areas that you are lacking, but as I said when you are using it, it tends to hang on the page and if you have a lot of traffic going to your site it's not a very impressive way for a first impression. Quantcast allows you to see what your website is perceived at by your actual audience.
the alexa rank is irrelevant .. and it doesn't update daily .. you should ignore it put a statcounter code instead on your site .. that should help