The difference is that Bahn.de gives 'non-stop' Amsterdam to London times where Eurostar gives 'change at Brussels' times.
Where I only to go as far as London I would book a later in the day option and take the change in Brussels. But as I want to travel on in England, a good option from an early direct from Amsterdam looks like a good connection. But this will not work if I have to make my way to Brussels to catch that Eurostar train.
I have checked an earlier question about the opposite direction of travel, but nor that question nor the link to the Man in Seat 61 give the answer I am looking for.
When do the direct trains from Amsterdam to London start?