Hi Falko, I've been on vacation since then, so couldn't answer. I just resolved the issue. Your hint about ENV pointed in the right direction. I have replaced the default webalizer with a newer one that installed to /usr/local. That path is missing from $PATH when run by cron. I added a $PATH variable to the cron jobs and it is working now.
I did not notice the problem on the other VMs because I had not removed the original webalizer from them. So, from cron the original webalizer was run (fine) and manually the new webalizer was run (fine).