Interesting question. Yes, as the answers state, there is almost no reason why the two programs should iterate at different speeds, especially when the compiler optimises the loop into an unconditional jump.

However, back in the day, with some CPU architectures, and with some fairly primitive compilers, it is conceivable for while(1) and while(something) to iterate at different rates. That is if the compiler outputs literal unoptimised code, and the something is a number large enough to require a larger instruction to initialise in a register than the number 1.

For example, the 68000 CPU instruction code has a quick immediate addressing mode, which can form the moveq instruction that will embed a constant between -128 and 127 into the instruction. It also has a slower immediate addressing mode that allows full 32-bit numbers to be sourced from an extra 32 bits tacked onto the end of the instruction. Therefore, while(1) {} could conceivably be compiled to:

  label:
  moveq #1,D1
  cmpi  #0,D1
  bne   label    (branch if not equal)

whereas while(200) {} would be compiled to:

  label:
  movei #200,D1
  cmpi  #0,D1
  bne   label

and this loop would run slower than the first.