My wife and I have been to Maui three times and Kauai three times over the past ten years. (We've also visited Oahu twice and the big island once.) After a lot of deliberation, we chose to invest in our first TS purchase at Kauai.
Here are the pros and cons of Maui and Kauai, IMHO:
* It is easily the most beautiful island. I know that is purely subjective and many here will disagree with me, but Kauai has an amazing diversity of spectacular natural beauty--from Mt. Wailele to the matchless Napali Cliffs to beautiful Hanalei to Poipu to Waimea Canyon.
* It's lush and green and made for adventure. If you like horseback riding or hiking through lush and pristine habitat, I think Kauai is unmatched. Kauai also has the only navigable river in all of the islands and kayaking the river is a wonderful adventure. The Napali Cliffs cannot be accessed except by trail or by boat, and either way of visiting is utterly exceptional and unforgettable.
* If you prefer quiet and pristine, the north end of the island is fantastic and the golf at the Prince Course is outstanding (the Prince Course is routinely rated among the 50 Best Golf Courses in the world by Golf Magazine). If you like beautiful beaches, the beaches at Hanalei and Poipu are spectacular.
* Three restaurants that offer truly exceptional meals in very romantic settings: 1) The Beach House at Poipu. It's run by the same owner of the famous Roy's franchise and both the food and the view of the sunset are unforgettable; 2) Tidepools at the Hyatt in Poipu; 3) Cafe Hanalei at the Princeville Hotel...the view of Bali Hai is enough to bring a tear to your eye!
Minuses of Kauai
* If you want nightlife, it's hard to find on Kauai. Kauai does not have anything similar to Lahaina, which Maui has. Of course, the major hotels do have nightclubs and there's nothing better than a walk on the beach after dinner. But the exciting night life is not to be found on Kauai.
* If you're bringing young children, Kauai does not have the kitschy kinds of activities like mini-golf or video games like Maui has at Lahaina. Even finding a movie theater on Kauai can be a challenge. On the other hand, if your kids like snorkeling with sea turtles or seeing whales up close and personal, either island is great for that.
Pluses of Maui
* I like what a previous poster stated here: "Oahu is the city, Maui is the suburbs, and Kauai is the countryside". That's a pretty good summary. Maui does have a nightlife and strolling the streets of Lahaina after dinner can be very enjoyable. The art galleries on Front Street are very nice and there are lots of diversions there that you can't get anywhere else outside of Honolulu.
* The golf is also spectacular, especially at Kapalua.
* The world-famous road to Hana is something not to be missed. It's beautiful, wild, stomach-churning. You need to do it once. Just make sure you have someone who can do the driving on the return, because you won't be able to have your head on a swivel to see the scenery if you're doing the driving.
* Haleakala Volcano is a fascinating national park, and a true highlight is getting there early enough to see the sunrise and then taking the bike ride down the mountain.
* The shopping at Whaler's Village on Kaanapali beach is great if you're into that. I'm not, but my wife is (and how many women aren't?). There's nothing comparable to it on Kauai.
Minuses of Maui
* It's become a little too commercialized, a little too crowded, a little too noisy in Lahaina, at least for my taste. This may be because I recently hit my 50's, but--to be honest--this was a negative for me when I first visited Maui in my late 30's.
* Maui isn't as lush and, therefore, is not as beautiful IMHO.
As I said at the outset, my personal preference is Kauai for the reasons stated. Your tastes may (and probably do) differ, so you really need to explore both to make up your mind. I hope this helps, and enjoy your first visit to what is truly Paradise. Ultimately, all of Hawaii is truly magical and I have every confidence that you will fall in love with it as we have.