Great gameplay, tons of secrets and easter eggs, SoR3 is what every future beat'em up should model after.
First, the soundtrack. At the time of it's release it was so different and out there, I know a lot of people who didn't like it. Very techno. The thing about it was the tracks for easy areas were soft techno tunes but the hard bosses and tougher areas had tougher, louder techno tunes. I personally thought it was genious from the beginning and personally wouldn't mind having a couple of the tracks on my iPod.
Secondly, the sprites/models. So vastly improved and one of the greatest graphical achievements accomplished on the Genesis. Even though the story wasn't exactly stupendous, the characters design is just so good you still care at least a couple times through. Then the story just gets old, but the coolness effect of characters like Axel and Shiva especially just stand out as two of thee coolest characters IMO. Their was quite a bit to their movesets (and quite a bit more when you had a six button controller) and all their special moves just looked so cool and flashy, definitely two of my favorite characters from that era. And to this day, SoR3 along with X-Men 2:Clone Wars are the only two games me and my buddies consistently do not get bored with, ever. Die Hard Arcade added weapons, but to be honest it was too easy, Fighting Force was cool with being able to pick up the cars and throwing them and stuff, yea it was pretty decent, but it's nowhere near as memorable as going through the game on hard. To this day, I've accomplished it once, with me having 0 lives and half a bar of health left and my buddy had died, oh yea I was Shiva too, which definitely helps.
The only thing I can knock this game for really is not being able to hit guys on the ground and wounded enemies hiding off screen if you looked at them, I really hated that more than anything. But overall, one of my all-time favorites. As everyone knows, the only beat'em ups worth playing are from the 8-bit/16-bit days, these new ones just aren't anything special whatsoever. But out of that whole era, Streets of Rage 3 was thee best and probably your best bet to understand why there was such a craze for these style of games.