From what I've seen, the 737, if it is properly stressed, will handle just as well. Don't forget, the P-3's four engines all turned in the same direction (if you're not a multi-engine pilot, ask one what this means), and there are, well, FOUR of the big, oily things hanging out there. That affects both "G" loading and rolling moment.
With two less engines, but with more overall performance, the 737 SHOULD do just fine. The P-3 started life as the Lockheed Electra, recall...a passenger airliner. We figured out how to do some pretty interesting things in it over 40 years, with sheer ingenuity. We'll do the same with a "P-8".
I also saw the argument, and decided not to chime in. I have decided that life is to short to argue procurement with couch potatoes on the web.