These three categories are not helpful when it comes to choosing your training site. They are proxies for the things you may actually care about: patient volume, patient acuity, patient socioeconomic status, state of the hospital facilities, number of consulting services, and hospital referral type (primary, secondary, tertiary, quaternary).
The county/community/academic distinction may hold more meaning when looking for attending positions, but even then it's only a proxy for more meaningful information.