I've heard they are both good.
I just ordered two Rugers. I was shooting my 9mm at the range, and had the opportunity to shoot a Ruger MKII 6 7/8 target pistol. The accuracy amazed me. It felt as if there was absolutely no recoil and the balance was great. That pistol made me look good.
After shooting that pistol, I had to have one, or two. Before I make any purchase I try and do some research. The one complaint I had about the MKII was the magazine release at the bottom. The MKIII pistols have a mag release in the familiar up top placing. Also, there are various differences in barrels. There are lots of articles on why a longer barrel length helps with accuracy. No need to repeat it.
I've ordered the MKIII hunter which has a 6 7/8 inch fluted barrel. I also ordered a MKIII blued with the regular 6 7/8 barrel. The regular one is about $200 cheaper and will be the workhorse. This will also be the pistol that I teach my brother to shoot with. The Hunter is the sports car.
One other thing to check out is the difference between the 22/45 and the regular MKIII. I like the regular MKIII but some might prefer the 45 feel and look.
I noticed in some of the earlier posts people complained about the magazine release, and the feel etc of the pistol. There are many variations. Just because one doesn't suit you, doesn't mean another variation won't be perfect. Compare apples to apples. IE not one with the 4 inch barrel and the other with the 6 7/8 and then claim that one gun is better.