I've seen a lot of bad to mediocre reviews on this series and I felt it was time it received a review that really actually does the show justice. If you're expecting it to be exactly like Primeval then don't watch the show or ignore the original while you're watching it, view it as its own entity. This is a spin-off of the original and therefore it will have its own story arc.
Some of the most common complaints I've seen is how different it is from the original and how it's 'just a bunch of people getting chased by dinosaurs'. Every show has to start somewhere and most of the reviews I've seen are from people expecting the characters to know exactly what's going on from the very beginning. That's not what happens they, just like in the first season of Primeval, are learning as they go.
This show has much better CGI than the original, granted the original got better graphics the longer it went it still doesn't compare to how well done the graphics are in New World. I was actually impressed when I compared them side to side. It's not easy making dinosaurs look realistic, but I think New World does a fairly decent job.
The characters all have a great amount of depth to them and I really hope to see a season two so their backgrounds can be explored more. There are also some great dynamics between the characters and it is obvious the cast has a great amount of chemistry between them. There are also plenty of witty one liners if that's what you enjoyed in Primeval.
On the downside the first few episodes are rather slow. It's needed to introduce the characters, but it can be a bit much if you're used to Primeval's quick moving plot, which was really only that way because each series was about six episodes long (New World has over twice that many episodes in its first season). After those first few episodes, however, it becomes a roller coaster ride that leaves you breathless and wanting more.