Hawaii's beauty is fierce, IMO. You have a lot of jagged, jet black lava rocks transposed against a glorious blue sea. There is more lava-strewn coastline than sandy beaches. The islands are bigger, the mountains are taller, and the weather is overall more temperate year round.
Hurricanes are prolific in the Caribbean, but IMO Hawaii is more inherently dangerous: the tides are stronger, the wind is fiercer, the ocean is rougher and colder (hence sharks), the drop off into the ocean is more sudden, and people often die from flash floods and getting sucked into blowholes, or getting tossed into the ocean by rogue waves or riptides. When they say never turn your back on the ocean, I take it very seriously in Hawaii.
But Hawaii is glorious. At night, it's soooo romantic. The entire island slows down. The ambience at night is incredible, with tiki torches, and meandering paths through beautiful landscaping, and soothing Hawaiian music always in the background. I love sitting on my lanai at night and just listening to the ocean, which seems to calm down at night.
The Caribbean is an entirely different animal. The 2 most beautiful beaches I've ever been to (Trunk Bay and The Baths) are in the Virgin Islands. The green blue of the Caribbean is an entirely different blue from Hawaii.
The beaches in the Caribbean are more numerous, more expansive (both in width and depth) and more forgiving on the feet. And the slope from the beach into the sea is much more gradual. The waves lap at your toes instead of knocking you over like they do in Hawaii. And the water is warm, like bathwater. Snorkeling from the shore is incredibly easy in the Caribbean.
The Caribbean islands are much, much smaller than Hawaiian islands, but much more numerous and clumped together. From most islands, you can easily island hop to another island via a ferry. In some places, you could easily kayak from one island to another.
In the summer, the mosquitoes and humidity can be bothersome. And, of course, you have an entire hurricane season that can wreck your plans. But in the winter, the weather is a perfect respite from the winters on the continent.
One of the biggest contrasts between the island is the people. The Caribbean islands are inhabited by former slaves, and there are still lingering effects of that racial divide. While xenophobia certainly exists in Hawaii, it is targeted more at people who want to stay; tourists are generally welcomed. In the Caribbean, there is a very palpable tension between the haves and the have nots. It's subtle, but it definitely exists.
For instance, in Hawaii, service people are slow because they're on "island time," in the Caribbean most service people seem defiantly slow. They seem annoyed that you're interrupting their day.
Another example: One day we were riding in an open air taxi with our friends. The black driver waved to every other black person he saw, whether they were workers or locals. He stopped to offer a ride to a local woman walking on the street, and didn't charge her for the ride. He never waved to a white person, even fellow taxi drivers. If you aren't paying attention, you'd miss it. But I did, and I felt a bit uneasy.
A final example: We were at the local grocery store, with its sky high prices. The cashier rang up a local in front of us. His dozen items totaled $10 or so, which was a fraction of what it should have been. Blatant but obviously tolerated.
The Caribbean is still worth visiting, though, so don't let that stop you from checking it out. It's just an entirely different flavor than Hawaii. Both are drop dead beautiful!