Try this:
Run traceroute on your ubu box to first determine if you are getting data from your ASA:
tcpdump -vvv -i src host and udp port 514
or
tcpdump -vvv -i src host and tcp port 514
Assuming you see data, then move on to the next steps, else you are either not sending logs from your ASA, you have a routing issue (which I doubt as you are able to ping your syslog server), or are perhaps running SELinux and are blocked?
If you see data, then your issues are with either your syslog-NG daemon, or its config, most likely its config.
You need to have syslog listening on the appropriate protocol, dependent on whether you are sending to tcp or udp; you can listen on both for syslog-NG. Also, aside from a listener, you must objects such as source, destination, log, filter, parser, rewrite rule, or template.
If you see data in tcpdump, then copy/paste your syslog-NG config file into this issue, please remove your comments.
... View more