For binoculars, the naming system is that the first number is the amount of magnification, while the second number is the diameter of the objective lens (the end facing whatever it is you're looking at). For example, your 10x25 binoculars would be a 10x magnification with a 25 mm objective lens. The larger the lens, the more light that will enter the binoculars (thus allowing you to see better) -- it is particularly good for improving your ability to see things in low-light situations. A 10x20 and a 10x25 would magnify the same, but the 10x25 would allow more light into it -- it would be easier to see the images, but the larger lenses also cost more.
Therefore, a 10x zoom would be similar to what to get with a 10x25 binocs.
As far as your cameras go, if all other options are roughly the same, I would, in a instant, take the 18x zoom. Digital cameras are nearing the point where the amount of megapixels no longer really matter (8-10 megapixels are roughly equivalent to standard film cameras, which are generally considered to be high quality), but the amount of zoom is becoming more and more important. I don't remember where I read it, but I just read somewhere that the camera companies are starting to work on improving the number of megapixels only because it sounds impressive to consumers (now with 20 megapixel resolution!), but they're really focusing on improving the zoom technology because it allows their camera to stand out. Lastly, if you haven't yet, check out the two cameras on www.cnet.com --- they're generally pretty good about fully testing electronics, plus lots of users should have given their opinions too.
Hope that helps!
