First of all, a poweramp is supposed to make things louder. But different architectures equal (slightly) different sounds. Add this to different designed preamps, and you will solve the secret.
Preampwise I am thinking more that it is more about the ear of the engineer than parameters.
There are bassmen that lust for an amp that behaves like "a wire with gain" for an absolute neutral sound. This says to me that any component of the amp does something with the sound, just like paper or coil resistors you are able to find in lots of old amps. Users of this old amps are sure that modern resistors won't give you "the sound".
My GBE (600/750/1200) and my Magellan are able to mimic the tone of my GK 400 RB when I twiddle the knobs a bit. But I can't get the tone of one of those amps out of my Gallien Krueger. I am thinking about a much more "powerfull" (a mighty tool, as we say in Germany)
Talking of "baked in - tone" I am thinking of Gallien Krueger, Ampeg, Aquilar, Hartke LH 500 / 1000 and Peavey. And Markbass. I think that Glockenklang - Amps do it as "neutral" as I am able to think of. Just have a look at the Blue Sky with its EQ that is switchable. This is not only a feature that allows you to take a look at what twiddeling with the EQ does to the sound, this amps sound fantastic with the EQ switched out. But maybe "too neutral" for the most people, because of the "poopie in - poopie out" - thing that will happen. For myself I want to hear the sound, the charakter of my different basses. So the Genzler / GenzBenz - Stuff is good for me.
As I like the Ampeg - sound, I've got the feeling that they make my basses sound like - Ampeg. This suits lots of musical styles, like my heavy - metal - band, and a lots of basses. There is no P-bass - sound like played over an Ampeg Amp. So I still have a SVP Pro and a Class -H Poweramp (RedRock M 4.5, Made in Germany, available complete linear or (stock) with a bass boost, 19 lbs, interesting poweramp, google for it), and it sounds as an Ampeg is supposed to. This rack for me is the better SVT 4 Pro. So in my opinion its the preamp that has the baked in sound.
Try this out at home! Use one of your amps as the poweramp (poweramp in), and use the "preamp out" of the other amps. Now listen, is the amp sounding like the preamp? Or does the poweramp affect the sound?