Higurashi and Umineko

Hello there!
Right now I’m on my way to finish some of the most popular VN I consider interesting and at this point in time I’m reading House in Fata Morgana. After that I would like to start Higurashi or Umineko. I heard that those games are connected somehow so which game should I read first and are there some things I should be aware of? I know that there are different fan patches that are highly praised.