On the contrary to what others say here, I say for the most part, the story is on par with the original and in some instances, surpasses it.
I do admit, the first few chapters initially confused me, given how the first manga finished, but in the grand scheme of things it wasn't really anything to worry about, and set the stage decently. Not to mention the fact this entire story is one epic journey of Alita's self-discovery and her past.
With that in mind, I believe Kishiro has done a great job telling the second part of Alita's story.
I must state, that I speak as someone who has read both stories recently, therefore you could say, I don't hold much bias with the original, which I suspect might be the case with some of the previous comments here. I'm happy to be proven wrong though for the aforementioned statement, if it may be wrong.
Spoilers about a certain character reveal below:
I also really loved Caerulla/Vilma's backstory