There are two big differences between the Pape felt and the kind of felt used after 1852 or so.
The first is that Rabbit fur is less resilient than wool, so the fibers are easier to compress, in a way, and for some reason the rabbit fibre has a different sound which is less hard.
here is an example on a modern Steinway: https://www.youtube.com/watch?v=YBdMg6MQbbU&list=UU1YXuoUQn9SlpZAVp3rrGFw
Steinway used rabbit fur for a period before the wars.. you can hear the sound is more mellow and less percussive.
The second is that the felt was felted like the damper-felt of the time, with very fine fibres (similar to fine Cachemire) in a random order, and it does not resist tension, like damper felt from that period does not resist tension.
The key to the sound is that the felt, being made of very fine and highly-crimped (curly) fibres compresses very easily, while at the same time being very soft. Pianissimo playing is very easy and mellow because it is soft and when playing forte, since the fibres are so fine and the felt has low density (24 grams) the felt completely compresses and couples the harder leather underneath. I suspect the lower resilience also permits a bright fortissimo, because it would take longer for the felt to expand to it's round, uncompressed, shape, I am just guessing on this last point.
The reasons they stopped using the gray felt, which was also used on Erards, it seems. Is that it wore-out too quickly.
I suspect that the use of a thicker fine lambswool felt, as used from the 1850's, was also cheaper.
today's felt is also different from the felt of 50 years ago in a similar way: the fibres used today are coarse and generally cheaper.
The most expensive wool is the wool with the finest, longest, most crimped (curly) fibres! this is probably why piano felt has gone in the opposite direction..
toning-down a hammer with coarse fibres will only sound dull and the sound will not be focused...
so that is perhaps why modern pianos get brighter every year!