The MEGA65 uses an FPGA implementing an enhanced 6502 processor, the 45GS02, that supports all the instructions of the C65's 4510, as well as being able to switch to 6502 mode, where we intend to have full illegal opcode support. The CPU currently supports 1MHz, 2MHz, 3.5MHz and 40MHz modes (the final top speed may vary around that 40MHz point. It was 48, then 50, now currently 40. The final decision will be made soon before release, when we have timing closure and exact FPGA part selection nailed down).
There is no "modern" processor. Just pure 8-bit. i.e., the MEGA65 is very different to the C64 Mini, for example.