The biggest reason to get RHEL is certification (assuming you don't need their tech support or updates). A number of third party vendors will only support one of the Enterprise Linux distributions (RedHat, Suse, Oracle Linux, etc). Now the technical differences between RHEL and, say Fedora, is that RHEL gives you a long time of getting bug / security fixes that are "minimally invasive", that is you can apply them and have a very good chance that your existing configuration and apps still work without a reinstall ore reconfiguration. (This is what is meant by "stability").

For personal use, you can get similar stability from either CentOS or Scientific Linux, although the bug fixes will lag behind Red Hat by a few days (although some critical updates have been released only a few hours after Red Hat).