Good topic. People tend to overlook competitive intelligence.
In my experience the best competitive overview is one that is paired with keyword research and done on at least 10 potential competitors at the same time.
In most cases you want to evaluate the market share or impact of your main competitors, and you're right, one or two "SEO metrics" won't give you an answer.
When I've identified 10 or so competitors, I use a tool that shows me what keywords each competitor targets organically and on PPC. There are half a dozen tools like that out there and half of them are rubbish but I'm sure you know which ones I mean.
Depending on how well I know the niche, this step also allows me to estimate how much $$$ they're making.
Metrics-wise, the metrics introduced by the two largest backlink spiders are increasingly helpful. I mean TrustFlow, CitationFlow and DomainAuthority.
Although, again, on their own without looking at the whole picture, they're probably not as helpful. I recently found a site that had DA9 and not a single backlink. Zero. Figure this? For fairness sake, the higher the DA is the more accurate it is.
Similarly to yourself, I'll also look at unique IPs, Subnets and Domains linking back. Not only it shows how SEO-ed the site is, it may also show spammy tactics.
Also with size of site. I agree, it may be a good metric in the context of niche research but equally, digging deeper may help you discover competitors' vulnerabilities that you can exploit. I always scan competitors' site with XENU (free tool & no affiliation, dear moderators) - helps you discover on-site issues. Basically, if you're evaluating potential niches, you want to be looking for places where the main competitor sites have shortcomings. It means you'll have to put in less effort in getting ahead of your competitors.
It's also interesting to compare the number of pages according to XENU with the number of pages indexed by Google. It may uncover sites with content issues.
I still glance at the toolbar PageRank. Yes, I know I should be embarrassed :)
Haha, I think we all have some old habits. I still check Alexa if I'm evaluating several sites within the same niche and all Alexas happen to be within the top 500,000 range. Of course, I don't make any decisions based on that. Just curious :)