There's intentionally not much difference in functionality at the moment.
However under the covers there's been a major re-factor. What was the FSR has been split in two to separate the "Deployment Engine" from the mechanics of doing file system deployment. This allows you to plug in your own types of deployment targets if the ones out of the box don't suit.
There's also a new wcm deployment sub-system built into the repository which contains another instance of the "Deployment Engine" so you can plug in your own deployment targets into an alfresco run time. It's a sub system so you can reconfigure and stop and start it though JMX without bringing down your repo.
The biggest difference is that the ASR is now obsolete to be replaced by the "avm deployment target." The avm deployment target has retained the old ASRs capabilities but gained the old FSR's capabilities like content transformation, pluggable transport protocols and callbacks. It is also much faster.
There's also a "filesystem" target built into the repo which may help with preview and testing.
Going forward, Alfresco 3.3 should introduce some more types of deployment targets which use this new framework.
