I just did an award trip DCA-JFK-LHR involving TATL segments on VS. You can't pick seats on delta.com for the VS segments; you have to call VS and get your six character reservation locator.

After I did this, they allowed me to select seats, but then they wanted to charge me $70 per seat for the "extra leg room" seats (which turned out to have less pitch than Delta C+); I had to wait another day for the VS computer to recognize my DM status and my wife's PM status to be able to book these seats for free.

Other than Clubhouse admittance and being able to use the VS "Upper Class" check-in counter and the special security lane, Delta Diamond and Platinum was not recognized by VS staff in LHR; the most significant benefit we were denied was priority luggage tagging, which almost caused us to miss our connecting flight at JFK.