Realistically... Ryu's mobility isn't really that much better than Kratos. Kratos has a more muscular build which generally means more strength in the legs, thus more speed. What Ryu has on him is the fact that he's more agile.
Well, this can go both ways.
Ryu has the better distance weapon for a one on one, but Kratos chain sword beats out all Ryu's close combat choices.
It really depends on Ryu's supply of ninja stars. He cannot wield more than 10, considering his outfit.
http://farm2.static.flickr.com/1163/1348465144_774cf90351.jpg
If he cannot score a fatal or debiliating hit with the first star, he's in trouble. The stars have an effective range of about 30 feet, meaning once he throws it, Kratos can close the distance before he can get another one ready.
Also, Kratos bow is way superior to the ones Pit and Yink uses. Likely effectiveness area is likely 60 meters or so, which gives him time to aim with one arrow.
This also means Ryu has to close the distance, which isn't favorable to him since Kratos has an easier time attacking him before he can use his stars if Ryu's advancing.
It's close, but I'd say Kratos would 6 out of 10 fights.
A historic ninja would destroy a historic spartan, though.