Both kern310 and kernel4 support Intel as well as AMD processors. In linux kernel there is only minimal cpu architecture that was set to be able to execute the kernel, that was PentiumPro, 586 :-) Any newer cpu is supported. I tested kernel4 even on i7, used to work while developing on core2quad 6600, core2duo 8500. I also tested it on amd x2 5600+. Amd 2500, barton core, is definitely supported by kernel4 or by Gary's 310 or any previous kernel.
Regarding supported CPUs there isn't big difference among different kernel versions. Newer kernel has optimisation for some newer processors. Difference is in supported hardware, like chipsets and controllers, kernel4 supports all the new sata controllers. It is based on linux kernel 2.4.37.9, previous versions (not developed by me) on 2.4.19. To use linux drivers, the modules, kernel version should match the modules version (modules have to be compiled for the same kernel version) There will be no complains when you insert the module.