Well it depends on money and lifestyle. If you are retired then you options are much better, but if you have to work then you have to worry about finding a job and The big island doesn't have a lot of jobs at all, its not very populated. So there is a much slower pace of life there. You will get to know everyone. LOL But for fishing and diving, its an excellent choice.
Oahu is like most other big cities. I say that because you really have to think of Oahu as one big city even though its not. There is much more to do and so the social scene is much better and the fishing and diving and great as well.