As far as I am informed the Nimrod was a better ASW *airframe* than the P-3 (at least for UK needs) but was more expensive, which may explain, in part, its lack of success in those competitions for exports. During the selection process for its replacement a UK built and updated P-3 was evaluated againt a similarly updated Nimrod and was found lacking. Of course the UK is a small country with a lot of coastline buying a few aircraft. Possibly a unique combination
The Higher speed was a real advantage to the RAF as it could reach an objective in less time and then once there it would shut down two of its engines for extended time on station. No doubt this is only an advantage where fewer aircraft are available and so would not bother the US very much, but its worth noting when export customers only buy a handful of aircraft. So with the systems being the same this would basically leave local suitability, cost and politics as deciding factors so I don't think an inherent overall superiority for the P-3 can be deduced from these sales to be fair. Either way I suspect there wasn't that much between them in capability.
Regarding the sidewinders - As I recall, Nimrods on patrol around the Falklands would frequently meet at quite close quarters with an Argentine 707 doing the same job for them, the sidewinders were fitted to discourage this, which they did. Once the armed Nimrod was deployed the 707 was never seen again. Job done. I wouldn't call that silly. It did lead to a rumour that the Nimrod v 707 was the' biggest dogfight in history', but it never actually happened.
In terms of systems there was actually quite a lot of commonality between the P-3 and the Nimrod MR2 so there is nothing to choose there, though of course the Nimrod had the huge 'Lancaster-esque' bomb bay.
Airframe maintenance is something I would know nothing about however so I can't offer an opinion there. If victory does indeed go to the last man standing then don't forget the Nimrod MRA.4 will be contemporary with the P-8 after the P-3 has gone.
I am blown away that a NEW version is currently entering service of an airframe that first flew in its original form in the 1940's!! That seems surreal, and is a ready answer to those who describe the DH Comet design as a failure
Here is a nice pic of a shiny new MR/A.4 to cheer up those sad at the passing of these old ladies. The real shame here is that Govt penny pinching has led to the tarnishing of the reputation of this fine aircraft and needless loss of life. But thats another story of course.