Based on what I know of the 1918 pandemic, I can think of several reasons:
1. Mexico City is much more crowded that US cities — even cities like New York City. More people closer together equals greater numbers exposed.
2. Personal distance in the US is wider than in Mexico (or virtually anywhere else in the world). The closer you are to someone, the greater the chances to get exposed.
3. I would bet that more Mexicans (even in Mexico City) live in closer proximity to more animals than in the US. Flu gets really deadly if it moves from one species to another. (This is one reason why so many influenzas come out of China — people living very close to poultry.
4. Influenza viruses love to swap. When two different strains meet in one body they trade bits of RNA. This creates a new type of influenza, which immune systems may not recognize. The result is deadly. (Note that 1, 2, and 3 give greater opportunities for this to occur.)
5. The average age in Mexico is lower than in the US. One of the reasons that influenzas get really deadly is when they trigger an overreaction by the immune system. Call it the “burn down the village to save it” syndrome. People literally drown in the products of their immune system going crazy. This overreaction typically happens in the healthiest people — young, healthy adults ages 20-45.
Note that this is not really a matter of health-care system, because for the most part, influenza is a battle between your immune system and the virus. There is no real cure, and most medicine (except for tammiflu) are ineffective against influenza viruses. Yeah, major hospitals help, but in an epidemic, you don’t have enough beds to provide really dramatic intervention in most of the cases. Being well-nourished helps, but only if you do not get some influenza that triggers an overreaction.
Stock up on bottled water, get tammiflu at the first sign of the flu, and hope you get lucky enough to be relatively immune or miss it completely.
Why bottled water?
I'm a goner if Cat Flu strikes.