Its almost an entirely different film, and IMO miles better than the actual movie. Although some of the problems are still there like the sexualised female terminator or how it is still follows a template of T2, but the overall script is much more action packed and stays true to the tone of the second film in particular.
Some of the big things that were better are:
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John having a normal life, but then being chased and then growing into an actual leader over the course of the film. He even has a cybersecurity firm, keeps updated files on Cyberdyne (although his employee misses the new Skynet project).
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They have another good terminator/bad terminator twist in this one and its even better than the one in T2 as the TX/T1-G actually tricks John into believing it by "saving him" against CSM-201 (still Arnold but with new features like quickly regenerating skin or SONAR/Infrared/Heat vision), and then fools him into activating Skynet and triggering judgement day.
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The shoe-horned love interest/Brewster character is killed pretty early on and Sarah is still her old badass self, although on the run due to being a wanted terrorist for Cyberdyne explosion in T2. Her role is a natural progression from T2 and she gets a really good sendoff.
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Silberman has a bigger role to play and this time he come to save Sarah instead. The supporting cast overall is much better and once John assumes the role of the leader, they all come pretty handy too.
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The TX/T1-G is an even better threat as it falls into molten steel early on and just swims in it. It is a machine that can change its molecular structure that has multiple states which are all great in their own ways. The way it mows down people is amazing even to read.
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The chase/action scenes are bonkers! Especially the ones early in the film. I wish James Cameron directed with this script, he'd have nailed it perfectly.
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Judgement day is sort of happening throughout the film, ofcourse heroes stop it in the nick of time, but it stays consistent with the message of the first two films. San Francisco is nuked for real this time.
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The exposition/breather scenes are really done well, and the film strikes a good balance of humour and seriousness without falling into a self parody or glum/preachy movie.
Some of the weaker bits it had:
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I'm not sure how a snarky Terminator would have played out, especially by Arnie. Sometimes it does go too overboard with its quips. Although its cool that it motivates John and there is a pivotal moment where it motivates John by one single comment and it works really well.
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The final act has a bit of melodramatic tone at times. Maybe some reworking would have fixed it but the dialogue is rough at times.
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Some of the call-backs are groan inducing. Another alternate power scene doesn't really work that well. A few made it to the actual movie too ("She'll be back").
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It still ends with "No fate but what we make" message, which can put some fans of the actual ending off, but IMO it is better as it stays true to the theme of first two movies.
Overall, I'd have much preferred this version over the actual T3.
Here is the script for anyone that has a few hours to burn, and is a fanatic like me.