I'm a Canadian expat who has been living in the US for 5 years now. Having talked to people from all over the world about how their health system is run, no one's system is perfect. But, I was very happy on the whole with the Canadian system. My dad had several heart attacks and cancer; his wife had breast cancer two years ago. IMO their treatment was speedy and top-notch. There isn't really any "rationing" for urgent issues, although some treatments that offer little benefit at great cost aren't covered. That said, depending on where you live there can be waits for "non-urgent" treatments (which can suck if you're an elderly person waiting for a knee replacement). I have no specific stats or anecdotes on those kinds of waits though. Another issue is that some places have physician shortages, although that's not because of any rationing, usually because there's just a shortage of either doctors in that particular specialty or doctors who want to live in the middle of nowhere. To me, these disadvantages - although real- are far outweighed by having coverage that can never be taken away and isn't linked to employment. It also costs less overall.
Re: physician choice, that's not something I ever thought about before coming to the US. Generally your GP is your entry point to care, and they refer you to specialists. I'm not actually sure that I believe different physicians have dramatically different outcomes, anyway, since there are so many standards of care these days. I think it is possible to get in to see particular doctors although I'm not sure how it's done - maybe you ask your GP for a referral to that particular person? And yes, clinical trials do happen in countries with universal health systems, maybe even more since less money is wasted on for-profit care.