Having tried both I finally settled on the use of a home server with a few vagrant boxes, live editing the same setup as production sold it for me. Albeit in my case all it does is dev, so the content is generally duplicated from elsewhere.
Home servers are not bad per-se. Personally, if I am fine with power outages, non-redundant uplinks, I'd just go with a 8 core cpu board so I can run proper virtualization. If your laptop is not powerful enough that is - there's a thing to be said for taking your dev environment with you.