For me, be it branded as a BA lounge or Aspire - does not matter, but from alliance point it would be a lost . My experience, both lounges are the same - just the branding was different and of course the slightly better furnishing of the BA lounge. The other difference was the staff of the BA lounge was much more pleasant compared to the Aspire staff and of course more BA specific information on boarding/delays/cancellation info.
From food and beverage point of view - both are exactly the same - mediocre food offerings and beverage. It looks like in the end, there would be just 2 main lounges in Schiphol (outside of the Privium lounge) - KLM operated or Aspire operated (which also operates the Star Alliance lounge).
Although of course I am curious why this decision was taken (if it's true) - as the OneWorld footprint at AMS is quite strong (BA, IB, CX, RJ, AA) - the BA lounge would have in some ways improve their presence and keep KLM/Skyteam on watch.
Cheers!