You're asking two very different questions here.
Regarding who's "better," that's completely variable from area to area, service to service, and person to person. In some areas private ambulances, even if they do not respond to 911 calls, will have very motivated, well educated providers. In some areas the ambulances that respond to 911 calls, private or otherwise, will have dumb, lazy providers. And vice versa of course. There is to much variability across the country to say definatively which is more prevalent. Nor does it really matter all that much beyond what you are dealing with in your own area.
Now, if you want to talk personal opinions, that's different. Based on my own experience, in MY opinion and in MY area, generally the non-private
providers are better. Of course, this is only my opinion; doesn't make it right, and since I still recognize that and understand that it very well
may not be accurate in a multitude of situations...it doesn't really matter that much.
As far as what you should do...that is entirely dependant upon you. If you have the opportunity to move into management, and that's something that you want to do, then you just need to decide if it's a service you want to be in that position with. You can always move back to being a field provider, and having a supervisory position on your resume is always a good thing.