I have no experience with the General Ultimax RT tires (standard touring all-season), but I do with the Ultimax HP model (grand touring all-season). They were a best seller and best price at the time when we bought new tires for my mothers 02 Galant and they grip awesome. They did excellent this past summer and winter. If it wasn't for the tire size which causes a lot of sidewall roll over, they would be even better. For an all-season, I was impressed in the cornering abilities.
The Kumho Solus KR21 is also a standard touring all-season, but rated very highly on Tire Rack in its tire category. I almost went with a set for my girlfriends car a few week back, but ended getting a different tire locally.
If you can bump up to the HP model, try to go with those, otherwise I'd take the Kumho KR21. They are rated slightly higher than the RT on Tire Rack.