In the frame of reference where the two charges are stationary you will see only the electric force, which is repulsive.

In the frame of reference where the two charges are moving you will see both the electric force, which is repulsive, and an attractive magnetic force (the electric force will dominate, but both forces are there).

The net force will be the same in both frames of reference.

This is all a consequence of special relativity.

As another answer points out, when you have steady currents in wires you get different answers. The wires in that case have overall neutral charges so the electric force is not a factor. The magnetic force, which results from the moving charges, is important though and so you get the wires moving towards each other.

In the frame of reference where the two charges are stationary you will see only the electric force, which is repulsive.

In the frame of reference where the two charges are moving you will see both the electric force, which is repulsive, and an attractive magnetic force (the electric force will dominate, but both forces are there).

The net force will be repulsive and will satisfy the relativistic force equation in both frames of reference.

This is all a consequence of special relativity.

As another answer points out, when you have steady currents in wires you get different answers. The wires in that case have overall neutral charges so the electric force is not a factor. The magnetic force, which results from the moving charges, is important though and so you get the wires moving towards each other.