I've owned the EF-S 55-250mm f/4-5.6. In my opinion, at half the price, it would be better value for you. There are several reasons why this is so:

1. The difference between EF and EF-S lenses. AN EF lens must project an image circle large enough to cover a "full frame" sensor or film negative (roughly 36X24MM). An EF-S lens must only project an image circle large enough to cover the Canon APS-C sized sensors that are approximately 22.5X15mm. Since the APS-C image circle is only about 40% the area of an EF image circle, this allows the lens design to be smaller and lighter. Another benefit is that some of the lens elements themselves can be smaller, and thus use smaller amounts of the expensive materials used in modern lens design. In the case of these two lenses, the 55-250 can use smaller amounts of higher quality materials and still be manufactured for a very reasonable cost. The 55-250, while not outstanding, performs comparably to the more expensive EF 70-300mm f/4-5.6 IS USM in terms of optics.

2. The difference between "full frame" and APS-C sensors. Although the focal length of a lens is the same regardless of the sensor size, the Field of View (FoV) obtained will be different. A 70-300mm lens on an APS-C body like your T3i will give the equivalent FoV of a 112-480mm lens mounted on FF body. If you need the extra reach this works to your advantage. If you need wider FoV, this works against you. The 55-250 lens on your T3i has the FoV of an 88-400mm lens mounted on a FF body. Unless you are trying to shoot close-ups from long distances, the 55-250 will give you more of the FoV you would typically use. Having a lens with Macro capability can be nice, but neither of these two lenses really offer much more than the other in that department. Unless you're always going to be shooting from larger distances, at half the price the 55-250 is a better value as a telephoto zoom lens for your T3i.

3. Image Stabilization (IS). Both the EF 55-250mm f/4-5.6 IS and the EF 70-300mm f/4-5.6 IS have it. IS lets you shoot at a slower shutter speed before camera shake becomes an issue. IS will not help you if your subject is blurry because the subject is moving too fast. The IS on both the 55-250 and the 70-300 are good for about 3 stops of shutter speed (Tv). This means at 250mm instead of needing to use a Tv of 1/400 sec or faster, you can use 1/50 sec and expect to avoid blurring due to camera shake if you are practicing good camera stability techniques when shooting. The EF 55-250mm f/4-5.6 IS has equal Image Stabilization at half the price of the EF 70-300mm f/4-5.6.

4. Your possible future upgrade path. In many cases it is wise to invest in lenses that you would still be able to use if you decide to go with a Full Frame body in the future. In the case of the EF 70-300mm f/4-5.6, I doubt you would want to continue using that lens with a high resolution FF body, even though you could. It just isn't a great lens optically. If you eventually plan to buy a Full Frame camera, you should probably consider the EF 70-200mm f/4L (either IS or non-IS) instead.