I can't really speak for all of Russia when I talk about medicine and education, because my travels have been largely tourism related, whereas my education took place in one of Moscows more prestigious universities. So I feel the need to note that this is my subjective experience, otherwise someone will always chime in and say "well yeah you live in Moscow thats the only place in Russia that isnt literally just a ditch hurdurdur" /endrant. Note to, my experience with hospitals in the U.S. is limited to Florida and Texas.
I believe that Russia doctors are still some of the best in the world, oftentimes on par with their American and European counterparts, and we're lucky enough to still have free medicine available to all citizens. That in and of itself is a major plus. You never have to worry about insurance coverage and premiums or going bankrupt because of routine medical procedures gone awry. People visit their doctors yearly for free comprehensive check-ups and most work (besides things like dentistry, and medication of course) will come at no expense. My wife gave birth earlier this year, completely free of charge - though I did spend a few thousand dollars during the pregnancy on additional screenings and tests for the baby, this in private clinics, for additional piece of mind. Now my baby is visited every month for a check up by our assigned pediatrician (from our local hospital) again, free of charge. I love this system, and feel that it is the governments duty to keep their citizens healthy, and that hospitals and insurance companies arent entitled to make a profit of the ill fortune of others.
What Russia does lack though in medicine is often new or up-to-date equipment. There are some procedures or operations that you simply cant carry out in smaller cities because theres no equipment for it. People have to travel to central cities to get their treatment. On rare occassions, even Moscow hospitals will have to work in conjunction with japanese/german hospitals to treat a patient, if the technology or methods are extremely cutting edge.
From what I've seen in the U.S., there are much less hospitals, but they are very large and well equipped, and with (usually) very high-end diagnostic equipment. I'll skip the small private practices because they're equally useless (and dangerous) in the U.S. as they are in Russia.
If we could get a bit more modern equipment, and you could get a bit more free accessibility of medic aid, then I think we would pretty much be on the same page :)
Education in Russia is very thorough. In my school in florida we had levels, I'm not sure if this applies everywhere. You had the base level, where kids were learning just what was needed to get their high school diploma, then an intermediate program, an advanced program and gifted studies. Nobody forced kids into any one group - you could move back and forth according to your abilities. I loved that system, and studed in gifted cllasses. Here in Russia schools tend to force everyone to study at an intermediate-advanced level as far as math and science is concerned, which I feel shouldnt always be a requirement, as not everyone can keep up and get good grades, etc. Anyone who wants to study more can go to specialized schools (for all STEM fields, as well as humanitarian studies like history, language), but if you're lagging behind in a normal school it's easy for kids to feel inadequate!
I still feel we have one of the most time proven higher education systems. If you get into top level colleges for any field getting a degree is no walk in the park. Kids drop out each year like bad apples from trees and only the best get their masters, doctorates etc. Thats my experience studying in an "Ivy league" school in Moscow, though my Masters is in International journalism.
Small time and community colleges are useless for anything other than a formal diploma here in Russia, just like pay to win colleges in the U.S. (those informercial "universities"? come on..), but schools that fall into the top 50 in Russia all produce excellent experts in their respective fields.