As an owner and user of both the 450D and the EF 100-400mm, I can offer some help here. From a construction, durability, and handleability perspective, using the 100-400mm on the 450D will definitely not be a problem. Both the camera and the lens are durably built, and the lens mount can handle a considerable amount of rugged use and rough handling.
The camera does look a little small in relation, but thats just how things are with supertelephoto lengths. The lens (when purchased from a reputable dealer) comes with a tripod mounting ring, and when used in conjunction with a gymbal tripod head is extremely easy to use. Hand-held, the lens is not a huge problem. Weight-wise, it is actually surprisingly light, and you shouldn't have any trouble with it. From 300-400mm, it does get a bit long, but making sure you support the weight of it from below with your left hand on the focus ring is generally enough.
Regarding the focal length difference, it is about a two-fold decrease in angle of view going from a 250mm to a 400mm. That's significant, however it should be clearly noted that when photographing wildlife and birds, the extra "reach" provided by the 400mm is still not enough to allow you to photograph from any considerable distance. When it comes to wildlife, having 400mm of focal length at your disposal will certainly help you get "closer" without having to be too close that it becomes dangerous. When it comes to birds, you are still going to have to creep up slow and indirectly and get pretty darn close to get frame-filling shots. In many cases, you will still have to settle for partial frame shots and cropp during post processing. The 400mm will just make it easier and more likely to get good bird shots over a 250mm lens.
A few other notes. An important factor to keep in mind is that with a 450D body, you have an APS-C sensor. This cropped sensor has an effect on the field of view for any given focal length. This makes the 100-400mm lens effectively 160mm-640mm. This is in contrast with and effective 88-400mm for the 55-250mm kit lens. Having 640mm of effective focal length is certainly nothing to sneeze at, however it is generally more useful on a sensor with more megapixels (such as the 18mp sensor of the 7D.) Second, the optical quality of the 100-400mm is far superior to that of the 55-250mm kit lens. Functionally, the 100-400mm might take a little getting used to, as it is a push-pull zoom lens. Rather than turning a second ring to adjust focal length, you push the lens out or pull it in manually. A tension ring allows you to adjust how easily this is, and once you choose a focal length, it is best to tighten this ring down to prevent accidental extension due to a bump or by gravity when the lens is pointed down.
The Canon EF 100-400mm L series lens is a fantastic lens. I highly recommend it to anyone who needs a versatile supertelephoto zoom lens for wildlife and/or bird work. Combined with a 450D body, you might not be able to get the best photos, given the lenses maximum aperture of 4.5-5.6. Outside of brightly lit, midday sunlight scenes, I've found I have to crank my ISO up to 800 or even 1600. While this does make it possible to get shots in the early morning or around sunset, it does degrade image quality considerably. Noise is a real problem on the 450D body, particularly with green subjects (i.e. trees, grass, etc. when shooting wildlife or birds.)