JR Kyushu Pass or JP Railpass?

Hias,
I am doing a 9 day trip to Kyushu next year.

I know of the Kyushu Rail Pass for 3 and 5 days, but maybe it is better off getting a 7 day JP Pass instead?

I will pretty much cover most of Kyushu with rail wherever possible so it will pay, but not sure which would be best.

It is really impossible to say without knowing more about your itinerary - where you plan to go and how long you plan to spend there. But it is highly likely that 1 or 2 Kyushu rail passes will come out as a better value for you. The Northern Kyushu Pass in particular comes out as quite a bargain and almost impossible to not recoup the costs of it if you are traveling all over. Most of the best of Kyushu is in the northern half anyways.