Does sound go the same speed sideways and up and down?

Hi:

they both will hear it at the same time because the speed of sound is the same for both people However if the air is colder which make it slighty denser which will make the speed of sound to be a little faster but they will both still hear at the same time just a couple seconds little sooner.

Sound travel at 750 mph or 1,100 ft per second under the standard condition of 65 degree Farinight and at a pressure of 15 pounds per square inch

Speed of sound in air depends on its temperature and density, which in turn depends on its pressure and humidity. Holding all of these constant, sound travels at the same speed in every direction (effect of gravity is negligible).

Both hear it, if at the same distance...

The only difference will be if the temperature is different at the upside of the mountain vs the downside...

Temperature effects the speed of sound...

Air pressure does not...