The execution time of your loop() will be slightly longer when the CPU
runs at 8 MHz v.s. 16 MHz, but I don't expect the difference
to be significant. CPU-bound functions, such as digitalWrite(), will
run at half the speed. These functions, however, are quite fast. In
contrast, analogRead() is slow, as it takes roughly 110 µs to
execute, so ...
The loop function is handled like a while loop. This means, when the loop function finishes, some framework code is executed (very small) and the loop function is called again etc.
However, there are some calls that do not depend on the clock speed, the best example is the delay function, but also if you made your own check using e.g. millis ...