Awstats running on the same server as well? log analyzers are pretty much cpu intensive, in my previous farm, we run deepmetrix which then access each NLB node and sort of combine the overall log files for the website.
For you case, doubt you can find a time where 300sites are not active, and during cut off logs will be in both locations. yet anyhow you will need to find a 'good' time to switch it.
I'm curious though, per server and per site logging will have different impacts? the load will be the same to the server, it just that you now can have better control on when to run the analyzer and to which website it should query, right?