Have stayed at both, but have not done a family suite at ASM. We really like POR. We love the landscape, theming, food court/food options and entertainment. Now given the room type you have selected for ASM, the pros of having a separate room with a door for your baby to nap and having two bathrooms can be a big plus. I've looked at these for our kids as they're teenage girls and we really prefer having two bathrooms. So, you're really not comparing a regular room, if all things are equal in that regard, I'd pick POR hands down. But you'll have a lot more room/space in the suite vs the regular preferred location room at POR.
Neither resort have better transportation than another per se. Both are bus resorts to the parks so if you plan to bus a lot to the parks, consider the folding/unfolding of your double stroller. There are a good number of bus stops at POR, I think 4 whereas ASM is just one at the main hall. I think the suites are in the jazz and calypso buildings which are not that far from the main hall. You'll have more dining options at POR between Riverside and French Quarter with the food courts and dining at Boatwrights. You'll also have other activities on property available to you like a bike rental, fishing, etc. You'll also have access to the pool at FQ. I also know that ASM has been refurbished more recently than POR. Something else to take into consideration. Overall, we'd usually select a moderate resort over a value. If ease of transport is something you'd want to look at with the stroller and room for the pack and play, check out the suites at art of animation. They're likely more than the suites at ASM but with access to the skyliner, that might be more enjoyable.
