What is the correct / better way to align two connectors across boards?
The best thing you can do is use a single connector.

Verifying that the connectors are aligned on their nominal positions is only the starting point. Using a common origin for both boards will help. Double check that the part footprints are drawn correctly. Print out the two boards at the same scale and hold the stacked sheets up to the light. Everything good? The kinematic overconstraint means it's still going to be a pain.

Even with perfect alignment in the computer, real world manufacturing tolerance can make it hard/impossible to assemble two rigid boards with a pair of snug fitting connectors fighting each other. Some connectors are designed to allow for a small misalignment, but most aren't. If they are surface mount connectors, they will end up in slightly different positions and rotations from board to board. Same goes for through hole. Forcing a fit can easily crack solder joints and break traces off pads.