There are a few generalizations that most photographers agree on where it comes to the engineering of lenses. Heavier lenses typically contain more glass and therefore are engineered to a higher level of precision. Another one is, a shorter zoom range is easier to control for optical aberrations over its entire range than a lens of similar build quality over a longer zoom range".
So, yeah, the 70-200mm f/4L is better controled, optically, over its entire range than the more far reaching 55-250mm f/4-5.6 IS II but as cicopo has pointed out, you lose a bit of range on both ends in return.
Edited to add: I will not suggest that it is preferable to execute quality post-processing in response to less than desired results, but it is considered entirely acceptable. I spent 5 years photographing and printing images with my 35mm camera equipped with a 50mm lens. I experimented constantly in the darkroom with paper offering differing levels of contrast, dodging and burning images, and in general creating my images. No one ever suggested that my prints were anything less than genuine. Make your own art.
