I have both but their situations are so different that it's really hard to give an objective comparison.
The PATB-3 is in a Floydcaster and the Demons are both in mahogany Gibson scale set-necks, with one of them in neck position.
My mind tells me probably the PATB-3 is warmer, though it doesn't lack for highs.
Still, I haven't ever had the two in similar guitars so take that opinion with a grain of salt.
EDIT: I'd say the PATB-3 feels more vintagey, though I know that isn't what you're asking about.