It's the 2nd best Terminator movie behind the first movie and within my Top 56 movies. it's definitely underrated where as the 2nd movie is overrated as I think, while it used to be top notch for me, I find that lately (as of a July 3rd 2016 re-watch(Nov 27th 2013 was my previous viewing prior to this and at this point it was still a 10/10 but fell to a 6/10 in July 2016)) Edward Furlong etc brings that movie down. he worked better for me when I was younger.
I like Kristanna Loken as the main villain in T3.
also, like politicidal said, it seems that crane chase scene is better than most action scenes in general.
also, I would say I agree with the OP's comments except the "Nothing feels especially memorable in the way the prior films were." comment.
but I will say it would have been nice if Linda Hamilton was involved with T3 somehow as I figure, at this point in time, she's one of the stronger points about T2.
p.s. but speaking of Linda Hamilton, it appears she's involved with the new Terminator 6 movie. I don't see that being a bad thing.
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LOL, I actually liked Kristanna Loken as the Killer Female "TERMINATOR" and I also like how they briefly brought back the character 'Dr. Silberman' as well.