The biggest difference is that the Dot Com bubble was strongly focused on tech companies going public and pumping small cap stock prices up.
The AI bubble on the other hand is almost entirely being built by private equity, with the largest players all privately held but with large cap stock companies holding substantial stakes. Rather than a bunch of small companies getting pumped up stock prices of many multiples of their debut price then falling to zero, instead we have large cap stock companies bumping up their value substantially, but not by major multiples, while the actual value of the biggest players in AI are all speculative and can't be invested in by retail investors.
This is all by design, the financiers of the AI boom are well aware that a public stock oriented rush into AI for retail investors would lead to massive speculation and an inevitable crash, instead with all the retail money going into large cap stocks they hope to capture that value and funnel the money into buying long term gains by making sure that those big companies have some stake in the "winning" private companies. When the first big AI companies go bust, they will be consolidated into their investor groups and harvested for innovation to transfer over to the winners.
Overall this strategy seems sound to avoid a major retail stock bust, but isn't wothout its own risks, for example if open source AI ends up winning out and the biggest private players fall flat they could become toxic assets and drag down the large cap stocks, and thereby the Indexes and Index funds in favor of leaner players. In the current landscape, that would mean Microsoft going down with OpenAI while Apple goes up, Apple is waiting on the sidelines with a huge cash warchest, ready to buy.