Best way to control 64x64 rgb leds?

You will almost certainly need shift registers, and lots of them!

You either need 12288 outputs (1536 8-bit shift registers) or you need a multiplexed array (say, 32x384 LEDs or 4+48 8-bit shift registers) or maybe you can use 8x8 modules (64 of them) each with three 8x8 driver chips.