Someone says 'beat-em-up' and I think Streets of Rage, Double Dragon and games like that. I wouldn't even put Golden Axe in the same genre personally, I've always called it a hack-em-up. I make the distinction simple, if I'm punching, kicking or headbutting you as I move through the level, it's a Beat-em-Up, if I'm using weapons primarily, then it's a hack-em-up or shoot-em-up. The only recent Beat-em-up I've played was Sleeping Dogs. It has evolved, from Streets of Rage, but it's the perfect example of a modern Beat-em-up. DMC, GoW, they're not beat-em-ups at all, and never will be. Anyone who suggests otherwise is wrong. Why? Because you don't beat people up, you hack the crap out of them. The police would make a very real distinction between punching and kicking someone and hacking them to pieces with a sword then shooting them in the face, and the same should go for games.
I can't agree with lumping games like DMC and GoW in the beat-em-up category if 3rd person shooters are allowed a separate distinction. Back in the 16 bit days, they were basically the same games with either brawling, melee weapons or shooting weapons, but all had separate distinctions as Beat/Hack/Shoot-em-up, even the magazine publications at the time referred to them in this way, but today shooters are granted separate status but brawlers and weapon fighting games are lumped into one category? Naaah, sorry, it doesn't fly with me, they're different games, always have been.
“It's a movie. If you are going to believe and be affected by an action film, you shouldn't go to see Pocahontas because you are going to think you are a Disney princess” Chloe Grace Moretz, what a legend.