There are many ways to guess it I would mention them here.
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.
This is US centric and can be used to get even some more idea about the ranking of the site.
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 has launched Google Trends
to find out the traffic trend of your competitor.