Last I checked, a well configured NUC was nearly as expensive as a Mac mini and almost certainly slower than this. Depends largely on what you are looking for though. From the sounds of it the NUC also has a loud fan? (For some reason I thought they were fanless).
Yeah, both the Mac Mini and NUC have fans. The Intel NUC will definitely be slower and hotter (thus louder), but I still think it's a better choice if you specifically want to run Linux on it.
