I don't have it available yet, but if I had to guess I'd say the primary benefit is the algorithms that sort mail into these categories.

Unlike labels, which require fixed rules (or manual action) to place emails into them, the tabs sort emails algorithmically.

So I have to manually fix gmail's incorrect assumptions about how I want my mail to be filtered rather than manually put my own correct filters in place?

Doesn't seem right for me, but I guess I can see the draw for folks who don't want to deal with setting this stuff up themselves. (Which is probably most folks.)

This (incorrect assumptions leading to frustration) is definitely the most troubling thing to me about automagic solutions. I'm currently working on a project that incorporates this idea of sorting email into contexts (http://solnovus.com, not much info up as of yet), so we've been thinking a lot about this problem specifically.

We are working in user-defined contexts from day one (not all users fit into the 5-context model), but I think incorrect classification is the most important issue to address to minimize user frustration. We are approaching it by treating topic and context membership fuzzily and using graph visualization to aid in traversal of inexact queries.

I couldn't agree with you more: there are serious problems with binary membership and "automatic" filtering.

Do you find that you often have to manually fix gmail's incorrect assumptions about what mail you consider spam?