Sure, you can take the easy answer: older games had a better game play. But it's more complicated than this. Developers want to make games that keep the player interested. The more interest, the longer the shelf life, thus more money comming in from selling the game. Keeping that in mind, here comes reason 1:
1) Hardware
Back then, computers were very far from the computers today. The reolution of the display would usually be QVGA (320 x 240), reaching at most the full VGA resolution (640 x 480). As for special effects, bare in ming the resolutions mentioned above were used even before DirectX or OpenGL appear. So sorry, but no, no fancy graphics.
Now, in order to keep the players interested, developers choosed to add a lot of story to the games back then. Basically, poor graphics (although that was easily masked by the novelty factor of computer games themselves) led to good stories.
The benefit of this is that it cultivated certain expectations from the people playing those games. And this leads to the second reason why old games are better:
2) People
And I mean the people asking this question. Yes, you.
Because you've been playing the 'old games' that 'are better' than the new ones, your own expectations from a game were molded by those early games you have played. This means that from each game you pick up, you expect a story from it. And let's face it, most games today don't tell stories anymore.
Further more, your first gamming experience is the most influential factor. You played the first UT, and of course, all the following (UT2k3, UT2k4, UT3) suck. You played the first Half Life game, and HL2 just didn't bring the same satisfaction. Or perhaps you played the first AvP game on PC and felt depressed by the cartoony and lack of atmosphere from Monolith's AvP2.
The list can go on and on. The point is that the very first games we played imprinted in us a set of expectations. Expectations that didn't change in time.
But games do. They have to. Game making is a billion dollar business. So any developer will always target the largest market. That usually translates into an age segment. An age segment you are no longer in.
And since the kids today saw their first game using at least DX9 rendering, you can bet their expectation is of super cool graphics.
And you can bet they'll say that UT3, Crysis and the Halo series are the best games ever.
