With the exception of "Home Soil"[TNG1], in which Crusher instructs the computer to theorize on something, most of the time the TNG era showed us computers used in a way not dissimilar from computers today. You tell it to provide information, make your own theory or determination, and run with it. Or, via the vocal equivalent of clicking a "beam me up" icon, you tell it to do something it's already programmed to do.
In TOS, though, it seemed that the computer . . . for all its whirring and clicking . . . was doing more thinking. There seemed a more frequent use of computer theorization. For instance, in "Mirror, Mirror"[TOS2], Kirk poses a few questions to the computer and lets it do the theorizing, and even provide an instruction list for what to do with the theory's application. Scotty followed along with its reasoning enough to know he'd need some help doing the work, but that's it.
It may be that TOS was actually closer to future reality in that case. In a rather interesting article
, it's suggested that sheer volume of information along with mathematical correlation might allow for a computer that serves more as analytic theorizer than info-search-tool a la Google.
To be sure, this isn't necessarily a new idea. There have been many science-fiction stories about all-knowing thinking machines. Among other iterations, there was "Cyclops" from David Brin's novel The Postman
, which also featured a "data net" along the lines of what you're currently surfing.
But presumably, as we've gotten to know working PCs, the idea of what they're capable of has declined to some extent. That is the best explanation I can think of for the less impressive way they were written in the TNG era. To be sure, the computers didn't seem to be any dumber by any means, but they simply weren't asked that many theoretical questions as I recall.