Part of it is likely his maturity as a writer and the time he inhabited during Neuromancer, Count Zero and Mona Lisa Overdrive. A time where, much like Verne, the technology was both new and alien, yet it was becoming increasingly clear it was important and soon to be omnipresent. A world where literature dealing with this technology was necessary, but where it was still mysterious enough to have creative license. It's not bad, but it doesn't age well.
Otherwise you end up feeling that Da Vinci's writings and drawings have aged badly because helicopters don't use 'airscrews' the way he depicted them.
http://www.scienceandinventions.com/files/2011/04/da-vinci.j...
When the amazing thing is that he foresaw a vertical ascent airborne vehicle in the first place.
So it's not so much about the details, in your words 'how your grandmother things about computers', but how society would respond if computers had the capabilities that Gibson endows them with. That changes the picture quite a bit.