I guess I'd like to weigh in on this thread, since I use both lenses.
By the time I bought the 45-200mm, I already had a half-dozen legacy lenses in that range, but I wanted something that was convenient to carry in my camera bag and to use either while walking longer distances and/or while accompanied with other people (who might not want to wait while I set up a manual focus lens). I bought it just before a trip to Los Angeles & Las Vegas, and it served its purpose. I was never particularly impressed with the images, though, and never put it on the camera when I was at home.
By last month, I already had a fairly large number of telephoto lenses, among them my favorite night / tripod lenses (Nikon 105, 135, and 180mm) and my favorite day telephoto lenses (a Contax 135mm Sonnar and a 200mm Tele-tessar). Nonetheless, I really liked the convenience of the 45-200mm, so before leaving for a trip to Rio de Janeiro, I bought the 100-300mm.
It arrived as I was packing, and in the end I balked. (Rio is just now emerging from a high-crime cycle that has lasted a few decades). In the end I took the 45-200mm instead.
I got back this weekend, and immediately took out the 100-300mm to try it out. I'd agree with the folks above that it's not particularly sharp at 300mm (certainly not compared with the shorter legacy tele lenses I mention above). On the other hand, my only 300mm is a Zuiko OM, and it's such a hassle to use that I never take it out.
Here is a photo I took the morning after I got back, as the moon sets behind a hill in San Francisco:
And here are a couple I took that night, the first one at 300mm, the second at around 180mm:
I'll post some of the pix I took with the 45-200mm in Rio later, but for now I'm regretting leaving the 100-300mm behind. It's clearly a far superior lens, not only deeper and brighter, but also in the way that it renders the images. It's still not up there with the Contax lenses (especially the German-built 135mm), but it's much more convenient.
So here's my take: if weight (and size) is your primary consideration, go with the 45-200mm. If you're willing to carry the extra weight, the 100-300mm is the way to go.