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I am no expert on either but from what I have seen they are not really directly comparable. The area they overlap most is in probably in library management. Aperture is more aimed at the professional in this regard. Aperture's ability to correct images is more powerful and aimed at people working with RAW images. As such, it is more directly comparable with Lightroom than Elements or Photoshop. It works in a none destuctive way so you original file is left unchanged. Elements has more options for transforming and modifying images as distinct from just correcting them.
iPhoto is pretty good for something that is bundled with the OS. I love the book feature (to be honest, I bought Aperture mainly because you can do even better books). I would see how you get on with iPhoto first before buying anything else. Elements is available as a trial from the Adobe Web site. There is a new version (v7) for PC just out whilst the Mac version is still v6 so it may be worth hanging on a little bit. There are some good Aperture demo films on the Apple website and an Apple store will be happy to demo it for you