I played HERO for years until Mutants and Masterminds came out, and switched over after M&M 2e. (Note: I haven't played M&M 3e and can't judge how it stacks up.)
The two do very similar things - extremely flexible systems originally based in supers but usable for most anything, especially for higher-powered settings - but M&M dislodged HERO for me by doing those things faster.
I prefer the way HERO handles initiative and the way you can build a character around Speed. Varying the number of actions characters can take in a given number of turns can make screen time balancing tough, but it's much more interesting to me. I also like HERO's damage system a little better.
On the other hand, M&M is a lot faster in character creation, and a bit faster in play. More importantly, it has a robust, built-in Hero Point/Power Stunting system. I could backport that to HERO (and would pretty much have to to be satisfied with it), but it's an extra layer to explain to players, and making up powers on the fly takes long enough in HERO to make it questionably playable.
Still, HERO is a great system, especially considering what it was going up against when it came out. I much prefer it to, say, GURPS or BESM, two other contenders for a similar slice of the RPG pie.