The second lens is not wider. The 55-250mm is a telephoto zoom lens. It does not have wide angle. It goes from short telephoto (at 55mm) to long telephoto (250mm). This lens is great for making distant subjects look nearer to you like in outdoor sports, (well lighted) stage and some portrait work.
The 18-135mm is an extended version of your 18-55mm. They are both general purpose zoom lenses that go from wide angle (18mm) to normal/standard (35mm) to short telephoto. The 18-135mm has the added advantage of going further into long telephoto which the 18-55mm kit lens can't. These lenses can be used to shoot almost everything you'll encounter out there and the 18-135mm will allow you to shoot details just beyond your reach (very handy for tourists) and for shooting people of almost every kind (solo, small groups, large groups, half-body, whole body, headshots, etc.).
If you don't really shoot far all the time, the 18-135mm will give you the advantage of using just one lens for everything (no swapping of lenses anymore). It is doubly good even considering that it also has better optics that's why it costs a lot more. If you go this route, the 18-55mm becomes redundant (useless). The only disadvantage I see is cost.
The advantage of the 55-200mm is reach. It can get you closer from afar which is what most beginners tend to favor. Since this is just a telephoto lens, you will have to swap lenses now and then if you don't plan your shoot well. You will have to keep the 18-55mm kit lens for wide angle and normal/standard focal lengths (which from experience covers more shooting scenarios than those that need long telephoto).
Another option, if you really must shoot from afar, is to get something like a 70-200mm or a 70-300mm even. Don't worry about the 55-70mm gap. You won't miss it (that's just a step or two forward). Now, if you want to have everything in one lens, consider the 18-300mm. The (huge) disadvantage of this super zoom lens (wide angle to super telephoto) is that optical quality is very poor. It's not a crap lens however. It has its uses like in journalism and for students.