I went to med school at a hospital within a hospital, but am in residency in a freestanding hospital.
Day to day life.... I see fewer residents from other programs in the freestanding hospital, because I don't bump into them in the cafeteria, etc. Our program certainly does more for us than my med school's program did, and part of it may be the fundraising structure of the hospital. And, of course, the volume is different. You'll see more at a freestanding hospital just because there is more room to see them.
The philosophy is also a bit different. At the hospital within a hospital, Peds is a very small part of the overall picture. In freestanding hospitals, the whole structure is based on taking car of children, so everyone has a focus in Peds, whereas you may get a good deal of cross coverage in an adult hospital (phelbs, RTs, pharmacists, etc). Which may not be such a big deal, but leaves more room for bad patient care.
Most freestanding hospitals are strong academic centers, which means you stand a good shot to place into fellowship, but I don't think you need a freestanding hospital to get a good fellowship.