I think last time I relaunched the site I must have just created a new GA account, but in retrospect that was a bad idea. GA allows you to maintain several of what they refer to as Profiles under a single Property, which means you can aggregate all the traffic to your various versions in one report:
The only change that you need to make to the tracking code is to make sure you select the “One domain with multiple subdomains” option in the Tracking Code section – this adds an extra line that allows GA to recognise that you want to track the traffic with a single property:
Copy and paste the tracking code into all previous versions of your site, and all traffic will now be tracked in a single report. Now you can do things like compare behaviour across subdomains: go to Content > Site Content > Pages, change Viewing from “Page” to “Other” and select Content > Hostname to generate reports like this:
This is just a few hours’ traffic, but you can start to build up a picture of comparative time on page, bounce rates, exits, and other aspects of user behaviour across your ‘same-but-different’ sites.