I will have to be careful with my comments as I'm still active duty. To that end my comments expressed here are my own and in no way reflect any stance or position of the US Navy.
Personally, I prefer the P-3 for a multitude of reasons most of which I'm not comfortable discussing in an open forum regarding capabilities and limitations of the two airframes. However the P-8 is an amazing aircraft that has for the most part been fantastically reliable for us, the P-3 is showing her age, I've had more in flight fires than I care to count, more three engine landings than I care to count, but it always got me home safe thankfully, there are several who weren't so lucky.
Things I can say, old airplanes have a lot more "extra" built into them. Just a few years ago a P-3 departed controlled flight and was recovered below 100' with a 7.6g pullout as recorded by the SDRS (structural data recording system) a system installed to measure airframe stress to analyze airframe fatigue. Would a P-8 have saved that crew on that day with the same demands placed on it? Not a chance, it would have been an aluminum yard sale. The short field capabilities of the P-3 are vastly superior to the P-8, specifically landing rollout. The P-3 is less susceptible to FOD damage at remote fields and less well kept runways due to its high mounted engine intakes. The P-3 has a longer unrefueled flight time and flies slower and is more maneuverable on station while conducting anti-submarine warfare. The P-3 has a broader range and larger quantity of weapons stations compared to the P-8. The P-3 is a TRUE ALL WEATHER AIRCRAFT, I've flown in and through some absolutely terrible weather they would've either broken the P-8, forced us down with icing or flamed out the engines. Once over the North Pacific we had all four props slinging saint elmos fire, throwing ice chunks at the fuselage and being shaken so badly by turbulence that I couldn't read my logs or the majority of my tactical displays, once again the mighty Orion got me home safe.
After all of that, what does the P-8 offer? Comfort is king on long missions and the P-8 wins this by a landslide. After a 10 hour mission (or more) on a P-3 you're physically and mentally drained from all the noise and vibration. I walk off a P-8 after a 8-10 hour profile feeling great. The P-8 gets on station faster and flies higher giving us the ability to get above a good portion of the weather we had to flu under, around or through in the P-3. The P-8 system integration and battle space awareness absolutely trumps the P-3 in nearly every way. The P-8 has the capacity to carry more sonobuoys than the P-3 which are expendable for tracking submarines so more buoys is always better.
My personal opinion is that the P-8 is a force fit solution to our needs, it's doing the job and doing it well. However most of the P-3 long in the tooth issues would've also been fixed with a newer engine and prop control system on the mechanical side and would've equaled the P-8 on the software side in terms of situational awareness and capabilities. The plane we needed was the Lockheed P-7 that lost the bid to the Boeing P-8. It was basically a larger, faster, more modern P-3, with all the P-3 benefits and none of the P-8 shortcomings. Sadly it didn't win the bid. I'm always happy to answer questions about my experiences but if things get too technical or specific you'll have to understand I won't be able to comment or answer some of those questions. To that same end please refrain from speculating about capabilities in this open forum. If I can answer it I will, to the best of my ability.
One last time, the opinions I've expressed are my own and in no way reflect the opinion or stance of the US Navy or any government official. I'm purely posting my personal observations and opinions.