The series is great for a "new version" of the story. Almost all of the characters are well written. Although, you can definitely see Riordan's later character influences coming out. Grover is much braver and more confident. He's more akin to the Grover in Trials of Apollo then Percy Jackson and the Olympians.
Additionally, many of the monsters have more depth then they do in the first series. This is also like Riordan's later books where most monsters aren't cut and dry evil. The complexity of the "monsters" is definitely a win.
Also, we see the negative sides of several of the gods earlier than the original series. Athena's flaws are quite clear, which I also like. Hermes was always one of my favorite characters in the books because he felt so much more human. The show does a better job of displaying these flaws in the other gods early. So they appear less like gods, and more like very powerful people who have emotions other than anger and love.
They have definitely changed the original feel, but managed to keep many of the same traits of the characters that are just a bit more developed this early in the story. While I do miss watching the characters grow, I also understand that it's hard to stay completely true to the book pacing with a television series.
One thing I love is they have a bunch of the small scenes from the book that were cut from the movie. Like Annabeth telling Percy he drools and the toilet scene. There are plenty of others in there for die hard Riordan fans.
They did change some major aspects like Sally's interactions with Gabe. Our theory, my family's, is that this is to prevent the VERY abusive relationship in the book from showing in the series because we don't want to normalize that dynamic. They do still keep Gabe as the manifestation of the prophecy, although I would have preferred the poker scene included. And they show him badmouthing Percy on television.
If you are just wanting the book in live action form, this is totally not for you. But if you enjoy all of Riordan's series (including Kane Chronicles and Magnus Chase) then you may very well enjoy the series.