I think Kakashi would beat Oro, as long as the fight didn't go over 15-30 minutes of actual fighting, also depending on the distance between them.
Long distance - Oro has the edge here due to summons, and to the time that it would take kakashi to close the distance. This is where Oro MIGHT be able to use Edo Tensei, which would need to be prepped ahead of time.
Medium distance - Kakshi has said to Naruto [when they were chasing Deidara] that he is a medium distance specialist. Kaskashi has the edge here with his MS. His sharingan will allow him to copy and defend against Oro's jutsus, and he could summon his nin dogs, which would be useful at this ditance, or in close range.
Close range - Kakashi has the edge here also. Strategy is as important as ninjutsus and taijutsu here. From what we have seen throughout the series, Kakashi is a better close range fighter than Oro. Oro and Kakashi plan well, although Kakashi has an affinity for planning quickly in battle, where Oro likes to plan in advance. Kakashi's chidori can't miss killing Oro when he uses it, or else Oro could counter atack and win.
We don't actually know all of each of Oro's and Kakashi's techs, but we do know that a lot of techs take time to use and/or prepare to use, which means that Kakashi needs to stay close to medium distance to Oro in order to increase his chances of winning. Oro seems to prefer fighting at longer distances, so that he can see how his opponent reacts, as well as being able to use the time that his opponent needs to close the distance to use other jutsus.
The longer the battle goes on, the less chance Kakashi has to win, since he does have less chakra than Oro. Kakashi plans like Shikamaru, though not as well or as quickly. Oro tends to plan in advance, as seen with his body switch jutsu, and his attack on Konoha-all planned long ahead of the events themselves.
Yes, I'm a Kakashi fan.