This post is not extremely well thought out, so please don't expect anything inspired. Since this site is not one to write actual "articles" on such subjects, this is more like what I would say to someone who is currently using the iTunes store.
If you don't know what DRM is, it stands for "Digital Rights Management," and it 'protects' the music industry by only allowing you to play a file if you are the one who purchased it. Whether or not you care, DRM hurts you. It means those files can only be played in iTunes or on your iDevice; that may be fine for you ordinarily, but think about it in the long run: if you run into a circumstance where you want to play that file in a different computer or program or device, don't you think you should be allowed, since you paid money for it? DRM is a cage that iTunes puts you in for no good reason; piracy is a different discussion, but if Apple actually thinks that DRM prevents or lessens piracy in any noticeable extent, they are dillusional.
If I remember correctly, iTunes also has DRM-less songs for about 30 cents more; this shows two things: 1, that Apple really doesn't care about anti-piracy since they still sell open songs, and 2, it's just a scheme to either squeeze more money out of you or keep you trapped in their box.
iTunes sells you a song at 128kbps, which honestly is not all that bad. But the thing about buying MP3s as opposed to CDs is that you lose the option of choosing your quality. CDs can be ripped at anything fro 50 to 300kbps, and MP3s are whatever you buy. This might not be a deal-breaker for other people, but for me, I think "Why would I want to buy something that limits myself?" That doesn't mean I want 300kbps MP3s, but higher than the very bottom of 'Acceptible' would be nice. Amazon sells at 256kbps, which is wonderful.
The iTunes store can only be accessed and browsed inside of iTunes itself. This basically just forces you to use their convoluted software whereas the Amazon store can be accessed by any web browser from any computer. It links to your Amazon account so you can add MP3s to your Wishlists and other nice features that come with an Amazon account.
4. [UPDATE 10-26-10] Safety
What happens if your hard drive crashes and you lose all the music you bought? Well, with iTunes, you are essentially screwed. Apparently you can fill out a form to let Apple decide if you can re-download the music that you paid for, or Amazon lets you re-download any MP3s, any time you want, no questions ask, from any browser, on any computer. Wow, Apple...you won't even let me re-download my DRM-ed music ?
To me, it's absolutely no contest. Why would I want DRMed, low quality music from a store built into an awkward application when I can have free, high quality music bought from a site that I can access anywhere, anytime?