The Nate is a great Fender P and I think it really does the mid-range growly-thing very well. For me though, the 1024 had the edge as it just seems to fill more space across the spectrum, especially with regards to the super-tight, well-defined low-end.
It's obviously a preference thing, additionally I'm finding that the relatively larger body size of the BB, especially the amount of space between the forearm contour and the P pickup (where I rest my thumb) enables a more comfortable playing position for my wrist, more similar in position to when I play my Jazz bass.