There were a lot of changes from gen 3 to gen 4 to gen 5 to gen 6 in graphics, controllers, audio, game design, genres, etc., etc. and it was all great to experience as it unfolded.
As far as graphics go, I specifically remember noticing back in 2002, playing a Xbox and thinking "what is the point of the graphics being shiny-er or sharper?".
At the time, I knew Xbox had graphical advancement beyond what other consoles were doing, but stuff like load times, and controller ergonomics were way more important to me so I would get any multiplatform games on GameCube and just get exclusives games on PC/PS2/DC (PS2 being my second most preferred, since it had the best controller, though load times put GameCube above PS2 for me). Xbox controllers have never been comfortable, so that was always a no go for me.
When the 360 and PS3 came out, I didn't see the point, it was the same games with a new coat of visuals laid on top, but worse because a lot of game studios went out of business, we got way way less quirky mid-teir games, and games focused more on cinematics.
I ended up playing more PS2 and PS1 games than PS3 games on my PS3 hardware.
I got heavy into PSP gaming in 2010, when I found out that is where a lot of the interesting mid-teir games went.
After a few years, I had no interest in gaming on a TV/monitor anymore. I got a 3DS and Vita and skipped the Wii U/PS4/XB3, left my TV when I moved, and eventually quit gaming for a few years.
Graphics mean nothing to me now, I put 600 hours into Stardew Valley. If it had PS1 low poly graphics, it would make no difference, I played tons of low poly PS1 games many times through on the PS Vita.
MK8DX with GameCube graphics would be the same game to me.
As far as hardware goes, I am much more interested in stuff like near-instant save/load times, no (or at least instant) installs, ergonomics, pocketability, battery life, etc.
Basically, if the game is enjoyable and the hardware "gets out of my way" as much as possible, that is all I really want.
