I have lived in America and in Europe, and have experienced socialized healthcare and American healthcare.
As I experienced it:
Socialized healthcare - No frills (shared a room with 5 other patients, had a metal hospital bed that had to be adjusted manually, etc.). Less expensive treatment options are tried before more expensive ones, even when that means suffering for the patient. Paperwork is almost nonexistent, and cost is usually zero.
American healthcare - My hospital room was like a resort (it was huge, private, had cable tv - there was even a mini fridge, for pete's sake). Treatment is whatever is fastest and most effective. Paperwork is nightmarish, and costs can be high even with health insurance. Because billing is so complicated, there is no way of telling how much expense is being incurred until afterward. Without insurance, the hospital will probably refuse to treat you at all.
Basically, if you're rich or have good insurance, then America is the place to be for healthcare.
If you are uninsured or poor, it is better to be in a place that has socialized healthcare. Your hospital stay may not be pleasant, but you will receive free, adequate treatment.