I remember using a simulated machine with with a minimal instruction set in university. In particular I remember that the instruction that consisted of all zeroes loaded was a LOAD instruction. So, if you made a mistake and began executing empty memory then it would simply keep executing until it ran out of address space.
x86 appears to perform an ADD on empty memory, so similar behaviour to the example above.
All zeros in 6502 on the other hand, corresponds to the BRK instruction which activates a software interrupt so executing empty memory quickly puts the machine in a known state.
My understanding is that 6502 was designed to be written by humans, whereas (at least modern) x86 is designed for compilers to output. Historically, when a machine instruction set is designed, how much attention has been paid to the specific representation each instruction has, given that it can have real effects? I've focused on what the all-zeroes instruction does because I expect that would be the most common instruction to be accidentally executed, but I'd be interested in considerations relating to other instruction representations as well.