I think the image quality of the 55-250 is about equal with the 70-300, at overlapping focal lengths. Look at these two comparisons:


70-300 (sample 1) vs 55-250 at 200mm f/5.6


70-300 (sample 2) vs 55-250 at 200mm f/5.6


The 70-300 is a full-frame lens, that's why it costs more for the same quality.