There is no difference between the air pressure inside or outside the
home. The only time it will change and only for a second is when you
slam a door or open a door quickly creating a vacuum or high pressure
cell.

Or when it is really gusty.

Or when you've got a whole-house fan that's seriously oversized.
Or if you've designed your house as a NBC shelter and are
deliberately producing overpressure through your filtration
system. Of course, that's about which SIDE of the
outside wall it should be on, not which wall.

But in any case, the barometer should be placed on the
same wall as the thermometer and humidistat,
which generally means on an outside wall next to
the window, but out of direct sunlight.