The new consoles use chips with all eight cores having the same design. Big.Little chips tend to have either only the big or only the little cores active at any given time. The PS3 did have SPEs which were of a completely different design than the one main core, but that is the really only time this has been tried in recent history.
Most modern architectures tend not to have different core running simultaneously. The main reason is that this setup makes scheduling a nightmare. Modern CPUs have to dynamically allocate threads to be executed on separate cores. When some cores are faster and some are slower, it is hard for the scheduler to figure out how to optimally allocate the cores without a thread stuck on the slower core stalling a process that a faster core needs to keep going. The PS3 avoided this by forcing the programmer to schedule tasks for the SPEs rather than having a scheduler dispatch threads to them.
For the record, I am referring to CPU execution core like the Bulldozer and Jaguar cores the OP mentioned. For this purpose, GPU shaders, H.264 decoders, cell phone radios, or anything else that doesn't host the operating system.