The biggest difference between Trinity (A10-5800k) and Richland (A8-6600k) in general is that Richland officially support DDR3 2133MHz RAM whereas Trinity officially supports either DDR3 1600MHz or 1833MHz (I can't remember). Most A10-5800k & motherboards should work with DDR3 2133MHz, but I have read that there are some cases where it will not work. I guess it depends on the specific motherboard model and the specific DDR3 2133MHz RAM make and model.
On average games played on a Trinity A10-5800k with DDR3 2133MHz RAM (Radeon HD 7670D) is slightly slower compared to a Richland A10-6800k with DDR3 2133MHz RAM (Radoen HD 8670D). Therefore, for the flagship models of Trinity and Richland there really has not been much performance increase at all. With both APUs using the same RAM, Richland only provides maybe 2% - 3% better performance.
To directly answer your question, the A10-5800k will give you better performance than the A8-6600k as long as you use DDR3 2133MHz RAM.