You don't miss a lot in terms of event data. However, DFM does make use of some traps to provide a more complete picture of what is happening on your devices (e.g. stack failures, interface flapping, etc.) as well as being able to provide some more real-time fault information. But DFM is mainly poll-based, so you're not going to lose a lot of detail.
If you find the syslog and automated actions are getting you the information about what's happening in your network in good time, then you will probably not get much more by sending traps to DFM.
