Among many many other differences, assuming your angle isn't to denigrate the Archive team, one of the important differences is that TPB makes no garantees about content availability. Information that you can find through TPB (they host magnet links, not content. magnet links can be used to find other who host content) is only available as long as those who are interested in the content are interested in hosting it. Conversely, the Archive people seek to ensure that content remains available even after everyone else seemingly loses interest in it.
It's something like the difference between your local used book store, and the Library of Congress. Or maybe the difference between the display cases of your local natural history museum, and the basement of the Smithsonian.
That and they primarily archive public domain material and abandonware (apart from their web archiving project). They really couldn't be more different.
I think simply disregarding the web archiving is a bit of a cop out. It's interesting though that for the most part, nobody minds them redistributing loads of copyrighted material. Here's some reasons that come to mind:
They web material was distributed for free in the first place. They're redistributing ad-ware, not stuff behind a paywall. (The same can be said of some TV shows and indeed I think TV show piracy if often met with a comparatively cavalier attitude.)
It's used as a measure of last resort. If I want to read an article from Wired, I'm going to try to find it on Wired -- or more likely, I'm going to Google it and get a link to Wired, and not the archive. It's only when it's unavailable from the original publisher or when I have specific historic interest that I end up using the web archive. The result is that publishers aren't denied their ad revenues as long as they host their material. Your abandonware argument translates neatly to the web archiving efforts.
They're archiving. This gives them a touch of academia and altruism that's casts them in a totally different light.
None of these things in isolation necessarily makes what the IA does entirely legit under current copyright law; they effectively operate in something of a legal grey area. But add it all together and not many people are going to get upset--especially given that they'll remove material if asked to do so.
