Me too...
But I think when I was a kid I only started to really care about video games because of games like Metal Gear Solid and Final Fatasy VII.
I had a Mega Drive (Genesis) and a SNES and I didn't care much about it, but on PS1, the presentation, the characters and plot made me fell in love with games.
I think that's the reason that after the Wii I never cared to try Nintendo games. These days if the game doesn't have an interesting setting(story, characters...) or doesn't have a good online portion, I simply don't care about it.
Sony mostly does exactly the types of games I want.
That's interesting because for me it's kinda been the opposite. Granted, I got into 16-bit gaming pretty much as 5th gen was going on, since that's when I was old enough to really have a console, and while I have gravitated to heavy story-driven games for a while, I'm more into shorter, gameplay-focused stuff these days primarily due to lack of time thanks to work.
A lot of story-driven games just feel like they take too long to start up and pad portions out with filler that is only fun in the sense that you know (or hope) it leads to a payoff rather than having a payoff right at the moment you're playing it. I understand that kind of game design and can appreciate it, but if I had to choose, thanks to my schedule I just prefer games where the focus is more on game mechanics and gameplay.
Oddly enough I think games like REmake and RE2 remake hit the balance between focusing on story/atmosphere, length, and game mechanics that reward skill level/mastery very well. The former is particularly interesting because that was almost two decades ago, yet they still managed to get it just right. You can still engross yourself with the story, the setting and the characters but not feel the game is denying you chances to push things at your own pace or skill level just to create a setting for its story. At the same time, that same pace is a reward for increasing your skill level with the game mechanics and strategies formed with them, in learning the game through playing it, which IMHO is how it should be. And very little if anything feels like it's there simply to pad out the play time.
If more modern cinematic games were like that, I'd be inclined to preferring them a lot more, but that isn't the case. And I think the reason stuff like REmake did it so well is because of Capcom's heritage as an arcade developer, which you can still see to this day. That's them coming from an environment where every moment of your game needed to be interesting or you'd lose a customer's attention. Consoles would give them some breathing room on those design ideas obviously, but at least with games like the old RE games and remakes, they still use it as their foundation.