Fairchild Semiconductor DM74LS161A datasheet wrote:
The clear function for the DM74LS161A is asynchronous; and a low level at the clear input sets all four of the flip-flop outputs LOW, regardless of the levels of clock, load, or enable inputs.
The clear function for the DM74LS163A is synchronous; and a low level at the clear inputs sets all four of the flip-flop outputs LOW after the next clock pulse, regardless of the levels of the enable inputs.
Since most NES boards don't use the clear input at all, both ICs are suitable for this purpose. For multicarts carts that use the CLEAR input to go back to the menu, you'd have to use the '161.