I have tried it both ways... several times ... and ended up with it combined. There are two main reasons.
1. My personal and professional lives are intertwined and there were too many spots where it became confusing whether it sat in my personal system or professional system.
2. I do not have any qualms about storing my system on my work system. I chose my work system because most things come in, especially electronically via email or project management tools, at work. So it was just more efficient.
It would be nice to have a separate lists and 'shut off' work by closing my professional system and opening my personal system but it simply is not that simple for my work-life. So I have one single system for everything, and I've found other ways to transition for work to personal life, and back.