Stay the night in Fukuoka or Nagasaki ?

hi
i will be going to Fukuoka, flying in from Haneda. On the next day, I will be going back to Osaka by train.

I intend to make a trip to Nagasaki with by JR Pass. I was wondering if I can get any input on whether I should arrive in Fukuoka, take the train and stay in Nagasaki, or should I stay at Fukuoka, visit the city and then go
to Nagasaki the next morning and return to Osaka in the evening?
any input will be appreciated. I know it's a short period of time, but thats all i have!

I don't entirely understand the context of your itinerary. So, I limit my answer to just the question whether Nagasaki or Fukuoka is more attractive for staying overnight.

I think that both cities are very attractive for staying overnight, as both have a very attractive range of dining options. But Fukuoka's food stands are particularly unique and can only be enjoyed in the evenings:
http://www.japan-guide.com/e/e4803.html

If you are going to arrive in Fukuoka in the morning, I would keep going to Nagasaki. Stay a night there, and get up early the next morning and see what you haven't seen of Nagasaki then head straight to Fukuoka, take a look around, then back to Osaka.
If you are short for time on the following day, maybe get back to Fukuoka late that afternoon and stay the night there instead.

There is no way you can take in both cities in such a short time. If Nagasaki is your main destination, spend the night there.

Personally I think the trip is not worth it. You don't have much time for sightseeing. By train it takes 2 hrs from Fukuoka to Nagasaki and to get back to Osaka from Nagasaki it takes 5 hrs with a transfer in Fukuoka.