For profit hospitals are notorious for short staffing, to keep those profits up. As to them having the best equipment, that is a myth. One of my jobs, for which I get paid a salary, is with a publicly owned trauma center. We have 4 CT scan machines, 2 MRIs, and a PET scan machine. For profit hospitals in the area provide a steady stream of patients for just those machines, because they are too cheap to buy their own. Part of the EMTALA law says the hospital has to treat you or transfer you to where you can be treated. For profit hospitals are just not going to spring for the cost of equipment to do a lot of procedures. Often, for profit hospitals specialize--- usually in cardiology, because a cath lab is cheaper to set up than anything I've mentioned so far, or oncology, because the infrastructure outlay is really not much higher than a community med/surg hospital. With only a few exceptions, for profits run a higher nurse/patient ratio than publicly owned hospitals, unless you count the VA.
Despite the advertising about their docs, it's the nurses that determine a good vs bad hospital. That's why there ARE hospitals--- because that's where the NURSES are. Look for a hospital with current "Magnet Status." That means they have a minimum amount of NURSE turnover, and that NURSES actually WANT to work there. Keeping enough staff and keeping them happy is very expensive--- another cost a for profit hospital is not going to spring for.
By the way, western trained MDs only utilize about 9% of the available bio-medical science in the treating of patients. They are generally ignorant of nutrition, herbal therapy, other modes of treatment like Chinese Medicine, Ayurvedic medicine, Chiropractic,, etc. Oh, and The effectiveness of those modes of therapy have been researched and found to be more effective in many cases than western medicine--- they have been researched in countries with socialized medicine, usually, because those countries are truly interested in controlling costs. Western medicine absolutely excels at what they are good at--- but if it can't be treated by cutting, burning (radiation), or poisoning, they simply have no idea what to do. One thing I tell my own patients: if you have a non-psychiatric condition that they want to treat with antidepressants, you need to look at a different provider.
Read "Racketeering in Medicine," by James Carter. If you have a chronic condition that seems to have no relief, read "The Web that has no Weaver," or "Between Heaven and Earth." Another good one is "The God Complex," by Chris Titus--- he actually first tried to publish this as non-fiction, where he named names, but the publisher wouldn't touch it, so he rewrote it as a murder mystery--- all the medical data is absolute fact, however.