Comparing EF-S 55-250mm STM vs EF 70-200mm f/4L pictures

Honestly it is difficult to assess the differences with the picture you posted.

However I own both of these lenses so I'll give my $.02 worth here.

At one point I had a 60D and 70-200/4L IS. I never really liked this combo because I often wanted the short end to be a little wider. When I had the chance to get a refurb 6D from Canon I jumped on it. The 70-200 works very well on this camera and for me gave me a more useful FL range. I sold my 60D and at a later date picked up a SL1. Then I got the 55-250 IS STM. I took some comparison shots on the SL1 with both the 55-250 and 70-200. I didn't do any sort of thorough evaluation, but to me there wasn't a huge difference between these 2 lenses on the SL1.

Where there is a big difference using these 2 lenses on a crop camera is the FL range. The 55-250 starts out at a more useful wide end and goes further into the tele range. This and the lighter weight makes it a great compliment to a crop body. Also the IS is every bit as good and maybe slightly better than the IS on the 70-200.

I also tested the 55-250 against my 300/4 IS. While the 300 was better, the 55-250 was very close and the IS on the 55-250 was greatly superior to the rather ancient IS on the 300.

If I just had a crop body I would just keep the 55-250. While pixel peeping may show some advantages of the 70-200 over the 55-250 in some cases, it isn't enough to warrant giving up the more useful FL range, lighter weight and maybe slightly better IS.

For me if I'm just taking my SL1, I grab the 55-250. If I'm taking my 6D, the 70-200/4L IS accompanies that camera.

Bottom line is the 55-250 is the best tele zoom for a crop body. Unless you need a different FL range or aperture, there really is no sense buying other lenses. The 70-200/4 L IS is a great compliment to a FF camera if the FL range and aperture fit your needs.