Usually you get a season of an anime before you get an OVA but Kyou No Go No Ni did things a little bass ackwards.
So the OVV of this sereies aired in 2006 through 2007 with 4 episodes. Each episode is is set up with a mix of short stories cut back to back so they felt like a bunch of 4 panel manga cut together as an anime. This new full season of Kyou No Go No Ni actually retells every story told in the OVA with obviously more content mixed in and shuffled around. Also with this being a full series the animation quality takes a small hit while the ecchi factor takes a huge hit. Most of the jokes are still there but instead of the generous abundance of pantie shots shown in the OAV we get flipped skirts with no visible panties… (sadface).
So pretty much your getting a retelling of the OVA with some new added content and a lot less fan service. Even with out the fan service the humor still comes through and even though jokes are redone from the OVA they add a little more humor to make up for the lack of ecchi. So if your pressed for time you can get your fill from the OVA but if you are craving a lil more, go ahead and give the full series a go.