Linux support for AMD's GPUs has not been progressing at the pace many users would like, though it is improving over time but that is not the same with their APUs.  Phoronix just tested the A10-7800 and A6-7400K on Ubuntu 14.04 with kernel 3.13 and the latest Catalyst 14.6 Beta.  This preview just covers the raw performance, you can expect to see more published in the near future that will cover new features such as the configurable TDP which exists on these chips.  The tests show that the new 7800 can keep pace with the previous 7850K and while the A6-7400K is certainly slower it will be able to handle a Linux machine with relatively light duties.  You can see the numbers here.

"At the end of July AMD launched new Kaveri APU models: the A10-7800, A8-7600, and A6-7400K. AMD graciously sent over review samples on their A10-7800 and A6-7400K Kaveri APUs, which we've been benchmarking and have some of the initial Linux performance results to share today."

Here are some more Processor articles from around the web:

Processors