The difference I see is that, conversely to websites like pets.com, AI gave the masses something tangible and transformative with the promise it could get even better. Along with these promises, CEOs also hinted at a transformative impact "comparable to Electricity or the internet itself".
Given the pace of innovation in the last few years I guess a lot of people became firm believers and once you have zealots it takes time for them to change their mind. And these people surely influence the public into thinking that we are not, in fact, in a bubble.
Additionally, the companies that went bust in early 2000s never had such lofty goals/promises to match their lofty market valuations and in lieu of that current high market valuations/investments are somewhat flying under the radar.