We have not stayed in either, but....I believe these are correct:
Island Palms
Free Wi-Fi
Pay to park
Pay for breakfast
Bayside Inn
Free use of lobby computers and printers
Pay to park $18
Free breakfast
Free shuttle AP, cruise terminal, Greyhound Dpt, Amtrak
That is some of what we look at when making the choices you are. Obviously, location, a most important factor, is based on what you plan to do. I through in the transport, as you mentioned perhaps not having a car.
As mentioned both of these places are quite nice and well rated by most. There is another factor we would consider, and that is location within the hotels. There is a MAXIMUM difference of views, access and feel within each of these hotels as well as, between them. Status might make a difference?