You would be surprised. I'm 6'1" and I thought I would need the bigger frames too but I ended up with a Trek 4300 (non disc) at 19.5". I did try the 21" and when standing over the bike the top tube was all up in "my junk". Of course, if you are going to go to an LBS and check them out, you will see which size fits you better. Trek does not offer the 4500 in a disc version. If you're set on disc brakes then that's a no go.
The fork on the Giant isn't all that great. The Trek 4500, Rockhopper Comp and The Iron Horse all have better forks. Personally, I think for the price, the 4500 has the best components but no disc brakes. If discs are a must and you are seriously considering the Specialized you linked despite the price I would take that over the Giant. Specialized has better brakes and fork and that's worth the extra bucks over the giant if you can afford it.
So my (probably unworthy) opinion:
If disc brakes are a must, I would go with the Rockhopper Comp Disc.
If disc brakes are not a must, then check out the 4500.