I think you have to separate competitiveness, prestige, and quality of training. Very difficult to assess differences in quality of training because it depends on so many factors (quality of PD, quality to didactics, access to zebras and referrals, but also level of autonomy). My hunch would be northwestern, CHLA and case probably have similar quality to training, but it's just so hard to measure and assess that you have to go with your gut on this. Now in terms of competitiveness, Chicago and LA are probably perceived by many people to be more 'desirable' (not by me, cleveland rocks) making them much more competitive. A look at their resident rosters will probably confirm this (much higher percentage of IMGs/DOs -- don't get mad at me, not making a value judgement). Finally, in terms of prestige, if you're worried about this you're doing it wrong. I know the feeling, but no one cares about this; go to a place where you think you'll get good training and will be happy. no one gets laid because they train at CHOP.
now, about case western, interviewed there and many of the other big kids hospitals. case definitely seemed smaller (not a standalone kids hospital if that's important to you), smaller program, older and less impressive facilities, and not in as fancy a neighborhood as the other two programs you mentioned. none of these should deter you from going there (and a smaller program might even be better for you). the interview day sucked though; this might say something about the quality and organization of the program, but I don't train there so this is speculation.
overall, i think you can be a good doctor from any of these programs. the key is finding a situation that will make you want to be a good doctor and happy doing it.
