My trip is over, so I thought I'd give some feedback.
On Big Island I was with Big Island Divers. Big company, well organised, nice people. The boats are full, but one time I remember we were 8 non-beginners and had 2 dive masters, i.e. two groups of 4. They send those up that run out of air early, but continue to dive with those that are better on air. They tell you a lot about their discounts, but it happened twice to me that they weren't applied. So when it comes to payment make sure to double check the invoice.
On Oahu I was with Kaimana Divers. Small company with less "bureaucracy", which also means that they swipe your credit card on a smartphone just after the dive and you don't get an invoice for your expense report
In terms of discount it was the opposite experience - they applied it without me even knowing they had such a thing.
The diving itself was pretty good. The reefs on Big Island were not as good as I expected and those on Oahu better than expected. I did the Sea Tiger wreck on Oahu twice, which was ok (nice wreck, good visibility). On Big Island I did the Manta and Blackwater dive, which are definitely a great experience. So if you're up for those, you must go to Big Island, but if you're just looking for reef diving, you're fine on Oahu only as well.