6.4s make the big power. Cylinder heads on them are terrible. Rocker Arms as well. When they break, they break BIG and cost a lot of $$$$$ to fix. Reliable K16 Injection pumps are just now becoming a thing and are still fairly new and not well tested yet.
On the plus side, they come with common rail injection but that somewhat comes at a cost because the factory filtration isn't great, very susceptible to water dilution and ruining the pumps/injectors. VGT compounds are nice, spool very quick. Very strong bottom ends, many people making decent power on stock rods. 5R110 trans can be good until a certain power level, lots of aftermarket options for it.
6.0s are older and cheaper now. They are the old Oil injection HEUI system obviously and take a lot more fuel work to make the big power numbers....However Jesse Warren, Jaran @ HDP and Charlie Keeter have done some really impressive things with them.
They don't have as terrible head issues as a 6.4 if you ask me, no D P F , basically the same trans, the 05+ still have coil spring front ends, pistons aren't prone to cracking, rocker arm wear is nothing compared to 6.4 rocker wear, and fuel system dilution doesnt seem as common on them. But its still a HEUI....