Just listened to the clips ...
Well, that was certainly enlightening.
In the same guitar and using the same amp & cab, playing the identical riff with the same mic/recording chain ---
The Nailbomb is more dynamic, with more space between the frequency ranges of bass, midrange, and treble.
The Painkiller is more focused, has a lot more lower midrange energy. It also sounds more compressed than the Nailbomb. It's not more nasal, but that lower midrange peak adds a good amount of 'chunk' to the tone.
And the winner is ...
To my ears the Nailbomb has more subjective power when you directly compare the two.
The Painkiller has a helluva lot more chunk and grind going on, however.