Your experiences are just that: your own experiences. They definitely are not universal. I was a bit younger than you, but all my siblings are older. I, the young one, got the Genesis and this new game called Sonic. My eldest sister, on the other hand, who was also an adult during this time, bought herself the Super Nintendo instead. I distinctly remember my other sister's boyfriend, who was some guitarist in his late 20s (or 30s?), and all of his friends playing Jurassic Park on the Super Nintendo, next to a huge stack of games. No Genesis in sight. My older brother and I played Madden only on the SNES.
In fact, as I got older during this time, I grew out of the Genesis. The Genesis was the platform of colorful sprites: Sonic, Earthworm Jim, Mickey and the rest of the Disney licenses were ubiquitous. And it reeked of 'tude, which was seen as less cool as the 90s wore on, something that the corporations were trying to sell us. Meanwhile, the SNES had some classic-looking games: Castlevania IV, Contra III, Gradius III, and Super Metroid were definitely not childish, and these were some of my early staples. For every chibi Mega Man X, you also had Demon's Crest.
I will say that everyone played on the Genesis when Mortal Kombat was released, but by Super Street Fighter II, the benefits of the SNES pad was apparent.
This isn't to say that we were all actively participating in some console wars. I never remember anyone being "Team Nintendo" or "Team Sega" growing up. We just went to houses to play that kid's games. If one friend had Super Smash TV, we went to his house for it. When another friend got the Sega CD, we went to his house for it.
And then the Genesis started feeling a bit irrelevant. Sonic 3 + Knuckles was cool and all, but hey, have you heard of RPGs? I discovered there were even more complicated games than Zelda, like Final Fantasy II and Secret of Mana, and despite the graphics of the latter, it was much more interesting than what I owned on my Genesis. So by the time the PS1 and N64 were getting their releases, the Genesis was rarely played. But not for any reason than that's just where my interests lied. The N64 (with Super Mario 64, Mario Kart 64, and especially Goldeneye) and PS1 (with Final Fantasy VII, Twisted Metal, and Oddworld) were the consoles to play (if we played any games at all -- most of the time, we did everything except play video games; I played football and band and was more interested in girls, bikes, and hanging out), and Sega was just forgotten, a relic of when we were young kids.
So yeah, your experiences might be true for you, but that doesn't mean they would have been shared by everyone else.