Vectoria,
That is a tough question and you would come to an answer based on what you plan on doing with the lens.
- The better image quality is in debate with a slight edge (but really slight albeit half the price) to the 70-200
- As for range, the 55-250 is the clear winner, and 70mm is a bit too long on our cameras so you will be changing lenses more often.
- Luminosity wise you are on deep decisions: the constant f4 of the 70-200up to 200mm is the clear winner, BUT the 55-250 has IS which the other lacks, so... more or less a tie, depending on what you shoot.
- Size wise is where your decisions are easier: if you want a light weight, easy to carry lens that you are comfortable with, the 55-250 is the better choice... with the 70-200 you will draw all eyes to you and people WILL get uncomfortable with you shooting at them. That is a given! The 70-200 is much heavier and bulky.
So, if you feel comfortable sacrificing versatility (better reach, more manageable, no Image Stabilization, and, of course half the price of the 55-250) for the slighter better Image Quality and the better build of the L lens, go for the L lens. Take into consideration that the IQ is really only slightly different and, in some cases (where slow shutter speeds are required) you will probably get better results with the 55-250.
The 55-250 is not what you'd call ultra small, but the 70-200 is really big! Here's so you can compare them side by side:

Image taken from:
http://www.the-digital-picture.com …oom-Lens-Comparison-1.jpg
As you see, there is quite a big difference. What do you see yourself using the lens for?
Rafa.