is there a automatic way to tell if the database update has any new information that needs to be updated in my favorite list?
Not really.
But, since you're a Premium Subscriber, set your "My RR page" to cover the counties and systems of interest to you. You'll see them tagged green for updated last 24 hours, yellow for updated within last 7 days.
I check mine, and often, it was just a 'housekeeping' change that did not require an edit or addition to my programming or Favorites list files.