JAL vs ANA for domestic leg of an open jaw

When I go to Japan I usually fly round trip from the US to Haneda and back, but for an upcoming trip I am considering an open jaw routing with a return from Fukuoka. Surprisingly, it is almost the same price as the round trip. (In the past I have looked into fares for an open jaw returning from KIX, and that was always considerably more expensive than the round trip.)

The transpacific flight on the return will still depart from Haneda (on Delta, basically the only airline I can use, given where I live in the US). But for the domestic leg from FUK to HND I could choose either ANA or JAL. Is there any advantage to picking one over the other?

Also, since the flights will be ticketed by Delta as a single record, and they allow 2 free checked bags on flights between the US and Japan, I am assuming that I can check two bags on the JAL or ANA flight, free of charge. Can someone confirm this? And since the domestic flight is on a different airline (and not a code-share, as far as I can tell), I would need to claim my bags in HND and recheck them for the international flight, right?

Thank you!

Either JA or ANA will work equally well when tying in with an overseas flight. I can't speak for Delta, but I've done it a dozen or so times on open jaws with other airlines, usually tying in with JA (domestic JAL). As long as the Tokyo airport was the same on the way out, I didn't see my luggage until the states (Fukuoka-Haneda-US or Fukuoka-NRT-US) after checking it in at FUK. I only have had to pick up my checked bags if I had to change airports in Tokyo.

This is helpful; thanks!