The same thing happened to us, pack and play first and then the crib at the same age! i tried to keep him in the crib but every time he would scream like we were torturing him and he would climb right back out.
We converted the crib to the toddler bed, just because it could but now he is in a full size bed and is doing fine (we too had a full size bed in the spare and a new baby coming and i didnt want to buy a twin!)
I think if you have the rails and he cant fall out, there is no difference between mattress! If you are worried, dont put the boxspring under it right away so its not so high
good luck!!