The answer is as easy as it is counter-intuitive: Tumblr is a New York company and Posterous is a Silicon Valley company.
Or, to put it another way: Posterous is an engineered product, while Tumblr is a designed product.
Posterous is extremely well engineered. There’s nothing wrong with it. Every single thing about it is well thought out. But it’s not just that it’s less pretty (though it is). It’s just not designed as well as Tumblr is.
I think it just boils down to Tumblr being perceived as cooler than Posterous. That coolness comes at a price.
How much of Tumblr’s content is just incessant reblogs of the same unattributed images? There are many Tumblelogs out there dedicated to just reblogging everything in sight. I’d imagine a “Public Dashboard” of Tumblr would look like the Public Timeline of Twitter… low on information, heavy on being utter shit.
Tumblr certainly needs to improve its engineering, and their API is currently languishing in a new revision that is both incomplete and naive. Their iPhone app suffers from bugs that should have been caught and fixed before revisions went to Apple for approval. They are far too focused on features when they should be refining or expanding the features they already have. It took them over a year just to make the mobile version of Tumblr.com offer much of the same interaction as the desktop version.
In spite of Tumblr’s flaws, it’s still popular, and I’d wager this is because the typical Tumblr user either doesn’t care about the shortcomings or doesn’t put much effort into using it. The only way for Posterous to gain popularity is for a large swath of users to flock to it, which is exactly what happened to Tumblr a few years ago. And for this to happen, Posterous would need to rethink their mobile apps, which are currently focused on publishing above social interaction.