I've been to the Big Island twice and Maui three times. If you want something with Big Animals then the Big Island would win as the night Manta dive is outasight, "place of refuge" is great snorkel/dive spot as last time we spent over an hour with 21 dolphins hanging out in the bay. On Maui off Molokini Crater we've seen Manta and every dive at least a few sharks. We've seen whales breaching.
There is plenty to do on land on either Island as well. Maui has the bicycle ride, coasting 38 miles down a mountain, the road to Hana, more beaches than the Big Island, waterfalls, Lahaina has a lot of places to eat.
The Big Island has waterfalls, Kona is much more quiet, the big attraction is Kilauea the volcano. Visit the shore where lava is pouring into the ocean as well at the top is Volcano house (tourist trap) yet interesting.
Looks like you'll have to choose between two great choices, but you can't loose. Save the other Island you don't visit for the next time.
Molokini - Maui
Big Island
Kilauea lava field and lava pouring into the ocean
shot taken while diving at Molokini
Place of Refuge - Big Island
Some have 15ft. wingspan