I seem to remember that the "2.0" version is significantly longer, but can't verify that. However, I've found a few interesting things, although it took me half an hour of searching to do so.
Do-Overs: 10 speculative fiction books that got major rewrites after they were published
The original version of When HARLIE Was One was a finalist for the Hugo award and coined the phrase "computer virus" for a program that runs on computers without permission. The 1988 version, When HARLIE Was One Release 2.0, was revised to include more accurate information about computer science.
However, I found more here: Templeton Gate review
It's fortunate for us readers that Gerrold decided to revise this novel. The first novel was written rather early in his career, and although a good story, had some obvious rough spots that were ironed out in the revision. Although the corporate infighting I outlined above is the overt plot of the novel, the conversations between Harlie and Auberson are the real point of the book, and those were much more clearly deliniated [sic] in the revision.
According to that same page, Gerrold changed the ending somewhat as well.
Since the original book was a fix-up of four short stories, it seems reasonable that there would be many problems that a new writer wouldn't be all that good at smoothing over. It looks like Gerrold smoothed out some rough edges, made the computerey aspects of the book more "modern" (i.e., got rid of stuff that didn't age well), and expanded the characters' conversations a bit.