Congrats Azeckel,
We just got back from Maui a couple of months ago. To me, you can't go wrong with any of the islands.
But I think it depends on what interests you and the Mrs. more.
First, I would start off by going to
http://www.hawaiigaga.com/best-hawaiian-island.aspx and trying the quiz there. This will give you an idea of some of the activities that you can do and will help narrow down your choices.
We love Maui for the mix of activities, shopping, dining, but more important to us are beaches and snorkeling (we go about 5 hours a day when there).
Kauai, while I haven't been there, is more back to nature, less touristy, more of the Hawaiian culture than Maui. My officemate has been several times and while she enjoys it, she told me that after 3 or 4 days, she is ready to island hop. But I do know someone that goes there for two weeks, and they love it and wouldn't go anywhere else.
Since you are there for seven days, maybe a 3/4 split. You listed golf/spa and beach time as the first items you want to do, that would be more Maui. But hiking is definetly more a Kauai thing, even though you can do it in Maui, you can't beat Kauai for unspoiled nature.
Good luck in your decision. I don't think a wrong choice could be made.