After about 8 or 9 cruises, we tried our first AI resort last year and had a marvelous time. We stayed at the Catalonia Bavaro in Punta Cana for a week ($2000 for 2 adults and 1 child, including air from Boston). We're heading to the Iberostar Punta Cana for 2 weeks in November ($3000 for 2 adults and 1 child including air).
Brief comparison between cruising and the AI:
Food - Cruise food is better hands down. However, we always found something to eat and enjoy at the AI. There were omelet and pasta stations that were great at breakfast and dinner, but we had them literally every day since the other food was just so-so. LOOOVED the fresh-squeezed juices that they made to order.
Beach - This is the best part of the AI. We rolled out of bed, headed to the beach, and sat around all day. Ahhhh. When we went to the beach on the cruise, we had to walk down the pier, manage an aggressive taxi driver, ride to the beach, and rent chairs. Then we had to watch the clock and make sure we were dry and ready for the cabbie to return.
Cost - Our experience at the AI was that it was truly all inclusive. No one tried to sell us the drink of the day, bingo cards, soda card, or photos. We chose not to do any excursions, as none seemed appropriate for our small daughter. Our only expenses were the tips we CHOSE to give to our waiters and maid. It was a treat not to have anyone expecting a tip at the end of the week or asking for positive remarks on a comment card.
Shopping - I had hoped to buy something nice in Punta Cana but there was really no opportunity. We didn't leave the resort all week, except to walk to a small market up the beach, where we bought coffee and a couple of souvenirs. There are far more and better shopping opportunities on a cruise.
Activities - The shows are better on a cruise than at the AI. But I noticed that there was more nightlife at the AI we went to. There is a big bar scene of people just hanging out and enjoying a cocktail after dinner. Not wild partying, but social, laid back and fun. We didn't participate as we had DD with us, but it looked like a good time. During the day there is an animation team that leads beach games, water aerobics, Spanish lessons, painting lessons, etc. You can also pay for excursions, such as a catamaran trip, parasailing, etc. Cost was on par with a cruise excursion, perhaps a bit less.
Sorry for such a long post. Whatever you decide to do, hope you have a great trip!
Thanks for all of the great info so far! I knew my BB buddies would have good experiences and advice to share! You have given me some great ideas as I begin researching.
) to schedule a vacation that would be cheaper than the cruises we have done. 
WE love love 
cruising but boy is it expensive during the summer months when we need to travel.
I know nothing about AI and you have helped immensely!!
