I love the Sega Genesis for just about all the reasons Jeff from Giantbomb does. That very distinguishable "Genesis sound" kind of fit with the whole early 90's vibe. I know it is technically a worse soundchip probably than the SNES, but like others said, going from the NES to the Genesis was like night and day, it really did feel like the next step.
Plus, I feel that the Genesis had all the weird but awesome game library where Nintendo had the timeless tired and true classics library.
Sports games tended to be better on the genesis as well, ect. Plus that gamegear, soooo awesome! Sure you had to invest in 3rd party rechargable battery packs, but for 1991 or whenever that thing came out, it felt like I was taking the genesis on the go compared to the gameboy.
EDIT: Don't get me wrong, I am not a crazy Sega fanboy, I love Nintendo. I eventually got a SNES during that time period (my mom thought the genesis was for grown ups from another parent of a friend like 2-3 years after me having it, one day I got home from school and found an SNES hooked up where my Genesis used to be... After wanting my mom to return the SNES and replace the missing genesis for like 6 months, I ended up with both consoles which wasn't a bad deal at all for a kid in grade school! Too bad I got the SNES like a couple years after it came out.