Higurashi brought us a new look on brutal violence and bloody gore. The second season shined some light on the, otherwise, nonsensical story about fate and parallel worlds. Higurashi Rei is really more or less an extension onto the story bringing a new "what if?" aspect to series.
The story is: Rika is living happily in her world after the events of Higurashi season 2. After getting hit by a truck, she wakes up only to find herself in another strange world. To Rika, this world strikes her as wrong. Some of the characters are missing and everyone is acting different, only to later find out that this is a world without sin. Rika tries desperately to find a way to go back to her previous world.
Rei has really nothing to do with the initial story of Higurashi. It's kind of like an expansion pack or DLC that gives you a new "what if?" after the fact. The first episode is more geared towards fan service as it's nothing more than the gang spending a day at the local pool. Episodes 2, 3, and 4 are where the main story is at, but they lack material because the majority of it is just talking and pointless backstory to Hanyuu's life.
The animation is quite good. There's no action, so the animation is pretty good for what it was. Definitely brighter and more vibrant colors add to the overall look making it look pretty good.
The sound is sub-par. Voiceovers are top notch like they usually are. The ending song is nothing memorable, but the beginning is a bit better.
The characters are really kind of devoid of their personas. Because the main focus is on Rika and Hanyuu, the other characters are more background noise than up center like they usually are.
Overall, Higurashi Rei is a decent watch for any fan of Higurashi. It's not really anything that you will go crazy over, but it will give you something different to think about.