SEO SpyGlass will harvest the backlinks to the competitor's site from the search engines so you will be able to see where they get their backlinks and maybe try to get links to your site from the same pages.
SEO SpyGlass has two that will be of interest to you: "backlink status" and "last found date". As you rebuild your project with time and update the backlink data some of the links will be added to your project while some links will be no longer found on the indicated backlink pages, so you can get an idea of what your competition doing in terms of link building - where they stopped getting links and when in particular. Generally this is as much as you can do in terms of tracking your competitors' activities.
As for the onpage optimization - you will need to use WebSite Auditor for that (
http://www.link-assistant.com/website-auditor/ ). It will analyze each particular page of your site to its' top 10 competitors for a given keyword, so you can see what kind of keyword density and prominence the top guys have to be on the first page. Naturally if you update your webpage reports in WebSite Auditor after some time you will see any changes the top ten have introduced to their sites.