Disc mower hitch style

I currently run a Deere 936 discbine with the standard clevis hitch. I am looking to upgrade mowers in the next year and I see they offer different hitch options. What are the advantages to the swivel and 2pt hitch systems? For our uses I usually only have the mower hooked up for a couple of days at a time. Any thoughts and experiences would help. I am not sure which manufacturer I would be going with yet. I was thinking New Holland until I read the NH 7220 thread. I do want rolls, hate the flails on my Deere.

Disc mower hitch style