By contrast, the Sinister franchise focuses explicitly on the hauntings by a lone demonic entity known as Bughuul, with a more intimate focus on that one demon’s effect on those around him and how he drives his child victims insane over long periods of time.
The Insidious series takes a big picture look at paranormal activity by offering up characters who understand the evil they’re facing, with Elise Rainier (Lin Shaye) representing the most notable of the bunch.
There’s nothing inherently keeping the storylines from these two franchises apart, and Jason Blum seems to think that there’s room for them to try and get a crossover made at some point.