No. In my honest opinion, the core gameplay was never good.
It's just that, it's even worse now. Because it was bad back then too, but right now it's as you said. It's own age age caught up with it, making it worse.
I had shitload of fun with various different versions of SA1 (SA1, DX, International). But SA2? IT'S HORRIBLE. EACH TIME.
I mean, it's just my opinion, so feel free to disagree, but...
The Tails and Eggman levels are no fun at all. The only kick I can get out of them, is when I play as Eggman, because it's Eggman.
Treasure hunting is boring and annoying. Which is strange, because I loved the SA1 treasure hunting.
Then there's the fact that Shadow is barely in the game, even though they advertise him as the next big thing.
In general, this game is a well made example of [tornado fang]ing up on the job, and poor planning too.
The only good thing about it, as stupid as it sounds, are the Sonic and Shadow levels. And even then there's not enough of them.
The only good thing I can say about it is this:
It's better than Shadow's game... which I outright despise.
The only thing I really disliked were the Tails and Eggman segments.
Otherwise, I liked all the other levels. I'll admit that I'm kind of a nostalgia fiend, so I'm a little biased. But I always loved running as Sonic or Shadow and jumping off a seemingly bottomless pit, only to land on a rail or platform. That took a lot of practice, and helped wonders with speed runs. If I recall correctly, Final Rush is the level that had those parts where you could fall far distances and land on a rail. The game never hinted or told you about these things, and It was awesome to fool around in those stages.
Treasure Hunting was fun. I didn't hate it, but I didn't love it either.
And as mentioned before, the Chao Garden. I spent SO MANY hours in that thing. Going from stage to stage finding animals to bring back to them. Overall, I personally think SA2 is a well crafted game.
As for Shadow the Hedgehog, yeah, I'm sure most agree almost any Sonic game is better than that piece of [parasitic bomb].