Depending on how much state your applications carry forward, I think killing the process is often the right thing to do. Otherwise, it's very easy to end up with connection leaks or just downright confusing state that can't always easily be traced back to what should have been an exception.

I run a node app that serves ~500M requests a day that is configured to die on exceptions, it just means that we do everything we can to prevent them (unit tests, linters, etc) and take them very seriously when they happen.