Tor actually does provide anonymity through onion routing. It's not effective against global adversaries, and doesn't claim to be. But it's hard to imagine how any low-latency overlay network could resist global adversaries. Chaff, caching and mixing would help, but they aren't that practical or effective unless you accept greater latency.
That's not to say they have the same threat model or provide the same protections. They are very different systems that have different properties - but at a broad-brush high level they both roughly allow you to publish stuff without people being able to easily track the information back to you under various assumptions.
> But it's hard to imagine how any low-latency overlay network could resist global adversaries.
This is a bit of an aside, but making a scalabe low-latency anonymous network is tricky. If you drop the scalabe requirement you can use dining cryptographers.
But with Tor, only clients (including onion services) host and access content, and they don't relay traffic. Conversely, relays merely relay traffic, and don't host or access content. Also, only entry guards ever see the IP addresses of clients. And they only see encrypted data going to middle relays.
So attacks like police have used against Freenet are impossible. Because clients never connect directly to each other. The closest analog is taking over an onion site, and then serving malware to users. But that's much harder than running nodes, serving child porn, and logging IPs.
Also, given that relays retain no content, operators have so far managed to escape liability.
A common definition of anonoyminity is that given a set of users, its impossible to determine which element (person) of the set did the action (published a document) [or have a better chance of guessing than guessing at random]. I think freenet mostly provides this property (with a bunch of devil in the details)