I wouldn't lean towards the problem with the actual ESX software or the underling hardware. This is more than likely a configuration problem. Perhaps a problem with sessions or with a corrupted table. We run ESX and any problem we've had has looked like software/hardware until we dig deep and determine the problem with the underlining configuration.
A couple examples:
A corrupted quiz table causes mysql load to spike as it reads rows without indexes thus causing apache to backup.
Sessions stored on a NFS server suffer from flocking due to poor NFS implementation. This also causes apache to backup and not respond to various requests.
We've had session problems in mysql database based on adodb library problems, see this thread, http://moodle.org/mod/forum/discuss.php?d=106108
My point here is that I'd look every other place before I'd look at ESX for the problem. Check your mysql slow querry log. Do some strace of your apache threads to see if there are any locks or disk read issues. Other system settings you changed when migrating boxes to ESX? I'd bet there is some underlining cause of the problem that is not hardware or esx releated.