I know I am someone who has actively asked Blogger for trackbacks since the new version came out. Trackbacks are a great way to get some traffic back to your blog, if you're someone who links a lot to other stories and your blog serves as a way of commentary on news broken on well known blogs. A simple link can do wonderful things. But the current system is inherently flawed.
As things stand now, a trackback is essentially a simple post to the target blog's platform's trackback RDF with the necessary details about the new post. If all goes well, a link back to that post is displayed in the trackbacks listing of the target/old post. The post can be manual or automatic, depending on what Blogging platformWordpress and Movable Type can essentially recognise links to send trackbacks to based on the links in a post. This solves the problem of trackback spamming a bit, but still isn't foolproof you use. Can you see the problem that arises? The post itself doesn't need to have anything to do with the target post, and trackbacks can be sent to all kinds of unrelated posts just to get links back. This is called Trackback spamming.
Trackbacks are almost like the taxi's of the blogosphere, which helps you jump from post to post of related content, that being the essential purpose of blogs. A glitch such as this can cause for a minor setback, but setback nonetheless, in a truly wonderful system.
How are Backlinks better
Backlinks rely on Google's indexing of your new post to display snippets of other posts which link to your post, which Google's crawlers have indexed. The only good thing about this is that bogus links don't show up. I believe Google filters pages from it's index (even blog posts) and hence, the blogs which are marked in Google's index as spam blogs, won't show up in your backlinks list. It becomes sort of an AkismetDeveloped by Automattic originally for Wordpress. Akismet is considered the best protection against spam comments and trackbacks. Via a public API, it has been extended to other platforms as well. for Blogger, albeit a less effective one.
New Blogger's storing of post content in a central repository (for faster serving), should also improve the speeds with which your link is caught and displayed by Google for the simple reason that it's easier for them to now keep a track of links (it's easier to crawl just the post content rather than a whole page). This also means that links in people's sidebars (like mine) shouldn't be counted as backlinks.
With new spam blogs coming up everyday, each one innovating on what we today know spam as, it will only become hard to filter them out. But we do trust Google, don't we? :P I can now see why Google has stuck with backlinks for displaying incoming links despite people requesting trackbacks. As a good alternative, Stephen's Blogger Trackback user-script does the job fantastically. But I'd still like a trackback 'sending' system for platforms which still rely on a manual post to their RDF, natively from Blogger.
Another point to discuss, which I didn't throw in initially (goodness knows why) is how Google tackles (or should tackle) the problem of spammy links. I think it is safe to assume now that Blogger serves all post content from a central repository, or what we can call a 'database' for ease. Now, since Google itself is storing all the data, they can easily check for links, and add the required backlink to the respective post. Hence, I don't think they do so much as a reverse-blog search, but rather just look at the new posts being added to the database.
So in effect, not only did the page serving become faster, but essentially all data coming from Blogger's side became faster, including backlinks. And this is ideal to keep spam links away, because just content is much easier to analyse for spam rather than a whole page. So this is a good alternative to Akismet which, as Avatar points out in the comments, is not available to many platforms, and is almost Wordpress exclusive.
So these should sum up why backlinks are actually better than trackbacks, but keep track of the comments as discussions say more than a one man's view. :)