I don't think it matters. Both are separate games

One is a murder mystery, the other is murder and a mystery

Good question! Both are independent stories that stand on their own, so if you don't care that much about getting the best possible experience, it doesn't matter.

Higurashi came first, and Umineko arguably has improvements in the writing department compared to its predecessor. Umineko also has a few easter eggs/references to Higurashi and a couple of things that happen in Higurashi are given much more meaning in Umineko, so if you're interested in reading both, and want to go for the best possible experience, Higurashi should be read first.