I was able to see the movie yesterday. So let me start of saying that the movie is amazing.
The tone and the visuals really hit different and it's a different Batman movie than all the previous iterations. Matt Reeves and Peter Craig really are a skilled writer set and the plot, the dialogues and even the humor are sharply written! Kudos to both of them. The score of the movie is amazing! Please do not listen to it before the movie. You need to hear and see the combination of visuals and the movie. It's full on amazing. Michael Giacchino has perfectly crafted a score for ages. In certain scenes I could feel my excitement and my adrenaline pump just because of the score. It's a very long movie, so it really does take its time in developing the story and the characters. I found myself liking the first 2/3s a bit more than the final stretch but overall it was amazingly told from start to finish.
The visuals, fight scenes and the camera work is very well crafted too. There's no shaky cam scenes, no fight scene is shot too close. And one particular scene had my jaw dropping.
I tried to avoid all the trailers and promo material to not spoiler the movie for me so I kind of went in not knowing and from the opening the movie turned out to be way darker than I expected it to be. But it's a good thing honestly and I am full on with it if it turns out to be a trilogy. And with that said people will try to compare it to TDK which in my opinion isn't fair because TDK was the second Part in a trilogy. This movie here should be compared to Batman Begins. And to answer the question. Yes I think it's better than Batman begins. And if Matt reeves can keep up the good writing and really develop the story even more we might have a better overall trilogy of Batman!
And one more thing which I find very important. Since the movie is rated PG-13 i would still advise parents to have a second thought about taking younger children to the movies. It's a very dark movie and very intense. I personally think it's even a bit hard for some teenagers who might react sensitive to the themes and scenes of the movie.