CHOP. Chop is internationally reknowned. It's my choice.
Both are excellent. I may be biased (I work at CHOP!), but I think CHOP is quite excellent across the board. Columbia has a wonderful pediatric program as well, so I would generally recommend whichever site is more convenient for you and your family.
Depends. It truly depends on what you are going there for. That being said, chop is ranked #2 nationally overall and in most specialty disciplines. Boston children's is ranked #1.
Subjective. Pediatrics is a huge field and there are sub specialist at all institutions that are leaders in their field. Depending on your child's issue and specifics, either one could be the right option.
Hmmm. Morgan stanley is an excellent children's hospital. But chop has been number one in the us for so many years i've lost count. I trained at chop, so i'm biased. But us world & news reports has rated it #1 or #2 in the us for the last two decades. If i lived in ny, i wouldn't go to philly, but it's just the best pediatric hospital in the us.