I haven't stayed at either resort, but I have lived on the Big Island and traveled fairly often to Maui.

I agree that you should account for the time and cost of interisland flights if budget is a factor. There's also a chance the interisland flight is delayed. I also agree that you'll want rental cars at both locations, especially if you're looking to explore the islands. Other considerations are gas -- it is expensive in both Maui and the Big Island -- and possible parking fees at the resorts.

In my opinion the Big Island has more things to see if you like the outdoors (Volcano, etc.), but it's also much more spread out than Maui. For example, f you visit the volcano from Waikoloa, it's at least 4-5 hours of driving round trip.

There's a small shopping center in Waikoloa Village with take-out food options if you're looking to reduce food expenses that should be relatively close to the Hilton Waikoloa, especially if you have a car.

If you or your wife has respiratory issues, the vog from the volcano could also be a negative for Waikoloa.

It ultimately depends on what you want from the vacation. If you're looking for an outdoorsy vacation, I'd spend more time on the Big Island, especially given its size. If you're looking at a lounge by the beach/pool vacation, consider more time in Maui.