There are many ways to guess it I would mention them here.

Alexa.com

You can always use to judge the ranking of the website and you get an estimate of ranking of site from the set of people who uses Alexa toolbar and it can a good estimate.

Compete.com

This is US centric and can be used to get even some more idea about the ranking of the site.

Yahoo

Yes you can also use yahoo to an extent. Siteexplorer you can use the get the idea about the backlinks to the domains and estimate the traffic quantum. As he is your competitor you can make assumptions based on your own traffic and links.

Google

Google has launched Google Trends to find out the traffic trend of your competitor.