I have the 70-300L and a 7D. Back in the day I had a 55-250 also. Here's my take.

Set both lenses at 250mm and f/5.6. That's the real comparison. If you don't immediately see a difference in the photos, send your 70-300L back. The real IQ value of the 70-300L should be shooting wide open, and in particular from 200mm-300mm.

Then you could set them at 300mm and compare You'll certainly prefer the 70-300!