The P-8, in addition to being faster than the P-3 and thereby having quicker transit times, will also have an added fuel tank. The stock 737 doesn't carry as much fuel as the P-3 does, so they added a tank (in the wing box i believe). 737 900ER carries 7,837gl (which is way more than other 737's), P-3 carries 9,200gl.
The P-8 burn rate down low is higher than the P-3 and you're not about to loiter an engine in a 737. The need to get that low will be mitigated by enhanced sensor technology. The reason the P-3 gets that low is it increases the accuracy of buoy drops and torp drops.
BTW, ship based torps are the same as the ones used by P-3's. Only subs carry unique torps as no plane or ship could carry a Mk-48 (well, a ship could, but it wouldn't do them a lot of good).
The P-8 has some disadvantages to the P-3, but overall it’ll be a HUGE improvement in Navy MPA capes. The P-3 is a good, solid, plane. It has tracked a LOT of subs and done a lot of very interesting missions throughout it’s life. I enjoyed flying it and would happily do so again but the P-8 will be a much better plane.
Most importantly the P-8 will have a flush toilet and a microwave.