Ultimately, I think it depends on your vacation style. Maui is more commercialized, with shopping centers, malls, and more "paid for" activities (like submarines, ziplines, sunset cruises). It's more family friendly, has awesome restaurants and easy hikes (Iao Needle, Haleakala). There's more traffic (but nothing like Oahu). It's a great place for a first visit. There are alot of "organized activities" available (Molokini crater, Pacific Whale Foundation and the Aquarium, etc). Maui is big, so research the area where you'd like to stay. The "feel" of each area is really different. Kapalua is more mountain terrain, complete w/Evergreens. Lahaina area is fishing port/town feel (but commercialized), Kaanapali to me feels like Laguna Beach, CA, and Wailea is more white sand/resorty.
Big Island consists of more outdoor activities that you must plan yourself; there are alot less organized activities to do.
Volcano National Park is amazing, hiking to lava at night is amazing, snorkeling at the Big Island is amazing, and sometimes when you're there you can drive for miles and miles and see nothing but black rock. When you're on the Kona side, it's a stark landscape until you get to a resort. I personally love it. You can spend days in Hilo (tropical landscape) or days in Kona (lava rock) or days on the Kohala coast (sandy beaches). Dining is limited, but very good (Brown's Beach House, Four Seasons stars and sand buffet, Merriman's).
The downside is it is hard to find middle of the road hotel options. It's either 3 star hotels which are pretty run down or 4-5 star options which are expensive. Try renting a condo. I recommend condos in the Waikoloa resort, and personally suggest Kolea (or Halii Kai). Sunsets are amazing on this part of the Big Island (can you tell I'm biased?).
Kauai is really laid back, less developed, more tropical (IMO) than Maui or Big Island. There's not too much off-resort dining (at least when I was there). The scenery is amazing, waterfalls are abundant, hiking is awesome. It's more of a honeymoon destination, and kids might eventually get bored. The mosquitos are thriving here...so you'll probably get bit, bring bug spray.
I would pick and choose which fits your personality.
One tip---make sure you do the hustle and bustle part of your trip FIRST.
I always forget how annoying it is when you get so relaxed on one island, you move to the next one (that's a little busier) and it's hard to get into the groove. (Once I did Big Island first, then Maui and hated it the minute we landed and saw all the traffic).
HTH