fundamentally they’ll both fly most things, but it’s the peripheral things where they probably vary more. I’ll try to stay with facts here as much as I can:
1 - license - PX4 is BSD, ArduPilot is GPL; this means that people modifying and then selling ardupilot are obligated to make their modifications open. ( but only if you sell product with ardupilot in it ). Any company who forks px4 is essentially closing their modifications off from the world and doing their own thing with it.
2 - ArduPilot runs on a bunch of hardware, including Linux. Last I heard px4 was moving to run on linux, but couldn’t yet. http://ardupilot.org/copter/docs/common-autopilots.html
3 - ArduPilot is more mature, having been in development for a longer time ( circa 2009 ). px4 didn’t exist till 2012.
4 - ArduPilot dev team flight test every single release, including having multiple beta/s before each release. We take crashes very seriously, especially betas, and won’t go from beta to release if we have known crash-causing issues. This takes a lot of time, so we typically release in the order of every 1-6 months ( vehicle specific ) for “release” builds that normal users fly. https://github.com/ArduPilot/ardupilot/blob/master/ArduCopter/ReleaseNotes.txt I’m not an expert of px4, but I see them dropping releases sometimes daily. https://github.com/PX4/Firmware/releases I don’t know how they flight-test all that. 
5 - Ardupilot is very proud of it’s real-world “position hold” (loiter) for copter/s, including outdoors, in the wind and turbulence. It’s a very complex algorithm that gives great results. I’ve never flown px4 myself, but I’ve seen plenty of videos, and I’ve never seen it perform as well as ardupilot does… unless they are flying indoors with nil wind, or have improved it recently.
I’m sure there’s more, but that’s some of the reasons I stay with ArduPilot.
Buzz