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Once inflated with regular, atmospheric air, the air inside the balloon will have a greater air pressure than the original atmospheric air pressure.
Air pressure, technically, is a measurement of the amount of collisions against a surface at any time. In the case of balloon, it's supposed to measure how many particles at any in any given time space collide with the wall of the balloon and bounce off. However, since this is near impossible to measure, air pressure seems to be easier described as density. The similarity comes from the idea that when there are more molecules in the same space, more of them will be heading towards a collision course with the wall.
The first concept of air pressure within a balloon that is necessary to know is that air pressures "try" to even out. With all the bouncing against the balloon wall (both interior and exterior) there will be a certain amount of expansion/contraction. As air pressure itself is a description of the total forces against an object, each of these forces, on the outside of the balloon, causes the balloon to contract a tiny bit, while the inside forces cause the balloon to expand. With this knowledge, one would immediately assume the a balloon with high air pressure inside would expand based on the high amount of internal forces, and vice versa.
This would make the inside and outside air pressures equal.