I think bikes are a lot like golf clubs: sure the older stuff still works fine but newer stuff usually makes it easier. Both industries have made numerous advancements over the years/decades. Fitting is also stressed much more now in both industries rather than buying something "good/close enough" in the stores years ago.

As far as bikes go in general brakes are better, shifting is easier, and weight as come down...that's not even getting into frame geometries and the increased variety of options. Sounds like you're in the "it's not bad but could maybe be better" camp so in your situation yeah I'd give new bikes a look. If you're able to find a couple in some shops give them a test ride and see how they compare. Chances are you'll find some things you like about the new bikes and you might find some things you still like about your old bike better. Plenty of people still ride classic bikes and don't feel they're missing out on anything; plenty of people ride newer bikes too, obviously. If you're questioning it there's no harm in testing the waters.