What I see in European countries, particularly UK most have families' centre but only live separately, having their own lives. Majority are quite closed families, visiting each others in the weekends or day to day to help out grand children (at least 50%). However there are some elderlies have to live alone, some have their son or daughter lives with and until these elderlies are very incapable to look after themselves that they have to move to old people's homes. It makes sense their children rather wish them to be take care by elders' homes. :)
The reality of American senior care is not as what they described. Most of senior in America are not financially independent and there are many abusive cases in senior nursing home. Many of my American friends' parents refuse to live in senior nursing home.