I'd take Puerto Rico over Hawaii any day for the following reasons:
-It's less expensive. It's true, I looked it up and I have been told this from people who have been to both places. The average rent for an apartment or a home in Hawaii is outrageous! I couldn't even imagine buying a place, the average price just a 1-bedroom studio is $1500-$2000, and that's not taking into account the price of food, gas, and electricity all of which are also more expensive in Hawaii. In Puerto Rico you can find a much more diverse range of housing options, though you don't want to live in the very cheap areas as they're probably unsafe. Food, gas, and electricity is a bit higher in Puerto Rico compared to the US because it's obviously an island and such things have to be shipped. However the Caribbean is not as isolated as Hawaii, and that cuts down on the overall cost of living by a lot. The cost of housing is far more reasonable in Puerto Rico than Hawaii, especially when you factor in taxes to which Puerto Rico also seems to be lower. Most of the people who I know that have lived in Hawaii only did so with some kind of support from the Military or the Government.
Rents for 1-bedroom dumpy studios in Hawaii:
Apartments for Rent in Honolulu, HI - 268 Rentals - HotPads
Rents for luxurious multi bedroom apartments and homes in Puerto Rico:
http://www.homes.com/rentals/puerto-rico/
-Friendlier locals. In Hawaii there is a large segment of racism among the native population towards white people, they call us Haoles. It's actually a much more profound problem than the Hawaii people like to admit, it effects everything from employment, to service, and there's even a massive problem in the Hawaii school system of white children getting beaten up (it's called "Kill a Haole Day, again look it up). This of course does not apply to every Hawaiian Native however, there are plenty of kind ones, but make no mistake racism is a big problem in Hawaii. In Puerto Rico I have been told that the locals are very friendly and treat you like a family member, that they're much more down to Earth and treat you as an equal. This is probably due to the Latin Cultural influence. However there are a few shady parts of Puerto Rico, mainly in San Juan, that are unsafe.
-It's not as isolated. This wouldn't be a problem if I was just visiting a place. However if I had to pick one to live I would say Puerto Rico as I'm a short flight (or boat ride) away from the US and to other Caribbean Islands (such as the Virgin Islands which you don't need a passport for if you are a US citizen). Living in such an isolated place like Hawaii would drive me crazy after a while, it's a long flight to get back to the mainland and it's not cheap either.
-I prefer Latin culture over Asian/Pacific Islander culture. Not bashing anyone's culture here, I just prefer Latin cuisine over Asian cuisine. I'm also a fan of Spanish style architecture.
-I have been told that Puerto Rico has better beaches, the water is warmer and calmer and the sand is snow-white and incredibly soft, like something out of a dream. Hawaii's beaches by contrast I have been told are rougher and the sand is more rocky, that you can't hang out in the water for too long before the waves give you a beating. I'm sure that beaches in both places are beautiful however.
-I love the Caribbean! I love the diverse cultures and the history that make up the place, it's much more diverse than Hawaii.
They both tie in natural beauty for me, they're both tropical paradises and I don't understand how anyone could honestly say that one place is "superior" in this regard. They both look pretty similar, nice beaches, vast mountains, hills, dense jungles, beautiful sunny skies, it's trivial to fight over such a thing.
Only major downside to Puerto Rico that I could see is you have to be fluent in Spanish. Hawaii does not have this issue. Though many of the PR locals do speak English. Also take into account that violent crime is higher in Puerto Rico, though this seems to be mainly isolated to certain locations of San Juan.