There is one big difference form the start: this is a copy, "too good to be true", while PTQ is based on a real Walter.
Also, a "Walter" is not a "standard" at all: each one is very different, as it was normal in this era of piano manufacturing.
I had the opportunity to record two different Walter pianofortes (one in Italy, one in France), and it was night and day: the first was very, very "bright" (almost too much) while the other was much more like the one in the video. But you could hardly believe they were made by the same person. Now, the restoration process was probably very different too... difficult to say which one was better done than the other.
This being, said, try playing this piece on the PTQ "Graf" (Beethoven owned one in his last years), it's closer to this sound than the Walter IMHO. You'll notice how clearly the low range is "articulating" the end of the first movement: I swear that Beethoven would never have written this on a Steinway D ! :-)