Statistically, I wouldn't know which Hospital has the advantage here. If we took two Hospitals with all the same doctors and all the same equipment available and all the employees were paid the same, then there really isn't a difference. But, if you throw in all the differences, then you have which Hospital is larger, which Hospital has access to the most MDs and equipment, which Hospital has the better employee to patient ratio. Which Hospital gets the patient in/out the most efficient and I could go on and on.
Yack59 makes some really great and valid points. Is your question comparing apples-to-apples, or apples-to-a-Porsche 911??
It's a very sad reality (in my opinion) that your "profit" hospitals do not look to kindly on the homeless, folk without insurance, poor, etc... (the hospitals claim they don't.... but they really do) The non-profit will take the homeless, non-insured, etc... quicker. So, this goes to what Yack59 points out. More money, better equipment. Less money, less equipment. It's that old standard: Supply and demand which we learned a long time ago.
As for which has the "better care given"?? I've been on BOTH sides of the "track" and I personally do not see any difference! Please always take this to heart: THE NURSES, TECHS, STAFF, ETC... RUN A HOSPITAL! NOT THE DOCTORS! Period! I've seen top-notch care from all staff members to the poor and homeless, and the rich and famous. It's the doctors (not all of them) that I've only seen the really crappy and bias care. Yes... this is a "soapbox" of mine. I don't do well with people who "think" they are better and above others. I can't stand the pseudo-gods! You know who I'm talking about, right? We've all seen them!
I have noticed a trend after working at 17 hospitals: I believe non-profits offer better patient care. The nurses seem to be less stressed and have a lower caseload. I don't have any statistical support, it's just an impression that I get. Both are concerned about the budget, rightly so, but the for-profit hospitals just seem a bit compromising when it comes to patient care.