Optically,. telephotos are inherently SHARPER.
But are, as noted allready, more prone to being susceptible to camera shake etc..
I'd check to see if the 70-200mm is sharper when mounted to a tripod and shooting something relatively close. If it's still not sharp you may have an issue
I agree with above. If you look at Canon MTF tables the teles are by far the sharpest lenses Canon makes.
I'm not so good myself.
