Does the 787 gust alleviation system make a more comfortable ride or for a more stable aircraft?
Both, but the improved comfort and stability are only side effects.

A gust alleviation system uses trailing edge flaps (ailerons, elevators and sometimes spoilers) to counteract local lift changes caused by flying through up- or downdrafts. The flap is deflected to change the local incidence and camber of the wing in order to reduce the change in lift due to gusts. This helps to lower the collective cyclic loads the structure has to endure over time and allows to use a lighter, less strong structure, or it allows to stretch out the inspection intervals for the same structure.

Since the structure will experience smaller deviations from the average load factor, you, the passenger, will experience a smoother ride in gusty air. In calm air the system will not make any difference.

Also pitch changes are smaller since the flight will be less bouncy and the tail surface lift can be smoothed out over time in the same way. Therefore, a gust alleviation system works similar to artificially enhanced stability.

A major problem is the unavoidable lag in reaction. If the bending moment in the wing spar is measured, a computer has to calculate the appropriate response, has to command changes in hydraulic pressure and flight control surfaces need be moved. By the time the flow around the wing is affected by the flaps, the gust has long passed. Therefore, it needs instruments like laser anemometers to measure the wind ahead of the airplane so the reaction can be timed correctly.

The answer to your last question would primarily be based on opinion, so I leave answering it to you.