I would do the parks. We have been avid
DCL cruisers and took DS last Sept for the first time when he was 14 months. Perhaps it was the fact that DH and I were so used to cruising on our own, but it was tough. Very fun, but tough. You have set dining times for dinner, which DS rarely made it through, he was too young to sit through the shows, the only part of the pools he could use was the Mickey ears along with the 10 other diaper-wearers and every other big kid running through it....(this was before the Magic went in Dry dock). The things that were great...he LOVED deck 4...as a brand new walker, he had the space to roam there and it was so fun to see him stare down at the ocean. The crew is amazing with kids...Flounders was great! The ease of character interactions at different locations on the ship. DS loved meeting Mickey and Donald with smaller waits (w/planning) than the parks. And the simple best is CC...doesn't even need explaining...we had a blast! Nothing takes away the fun of cruising, but things seemed soooo limited what he could do or what we could do as a family. It was a test cruise for us, which worked out well, because with #2 on the way, we know we will wait until the baby is 3 before we go on another family DCL cruise.
DS has been to the parks 3 times...at 6 mo, 14 mos and 20 mos. The variety of what he can do there is much better than on the ships. It is that simple...you can see a short show, you can ride on many rides that little infants and tots can go on, the parades, the fireworks, the variety of dining establishments that you pick your dinner time on (a must with little ones!) DH and I have also used Kids Nite Out for DS and it was a great way to have one night to ourselves....and by all accounts, DS had a blast, too!
Simply, having done both, we have decided the parks will be our route until 2012, when we will do our next cruise...sounds so far away!!! But then ALL of the family can get the most of the DCL experience....and cruise on the new ships! We have our next WDW trip planned for next year, when the DS will be 3 yrs and the LO will be 15 mos. I just think the flexibilty of the parks is the way to go for the tots.