If sicker people go into system A than system B, System B's outcomes will be better.  Scientific clinical trials all over the world are carefully designed to screen out this bias.  From Mind the gap: England found to be healthier than America

However, Britain's universal health-care system shouldn't get credit for better health, Marmot and Blendon agreed.

Both said it might explain better health for low-income citizens, but it can't account for better health of Britain's more affluent residents.

"It's not just how we treat people when they get ill, but why they get ill in the first place," Marmot said.

I agree with asdf's comments above.

Personally, if I come down with an illness, I wanted to be treated in the US.