I think the whole "Pick up and play" advantage for consoles was eroded with the advent of mandatory installation for consoles.

The only real advantages I can think of for consoles are parity for multiplayer in that everybody has the same system - you don't need to arse about with quality settings, we all get the same experience and for multiplayer nobody has an advantage due to having a better machine. Latency will always be a thing regardless though. I also think that the voice chat system on consoles is preferable to something like Teamspeak. I know someone will disagree with me on that, but from an all-in-one convenience perspective it can't be beaten.

From a sentimental point of view though I have a special place in my heart for console gaming.