Dampers are more effective than not having dampers and offer an improvement but are not the most effective solution. I suggest you consider a second furnace & air conditioning system if you really want this fixed right. Two story homes are unbalanced because heat rises and cold drops. Unless you have multiple thermostats to balance the air flow to the various parts of the two story house it will always be hotter on the second floor and cooler on the first floor.
The real answer comes from installing a second system in the second floor with a separate thermostat, ductwork, registers and setback thermostat. The main floor system must also be replaced to down-size to the capacity for the smaller square footage of only the main floor. The second floor system now can be “set back” during the unoccupied times of the day to conserve energy while the main floor continues typical operation.
We at Mosby Building Arts deal with this when designing the removal of the center load bearing wall between the living rooms and family rooms on two story houses. Many folks want more room and ask for a room addition. We as Architects offer the option of removing the center wall between the rooms to reclaim use of the living room. Structurally this is an easy task for our team … but the challenge is the many runs of ductwork inside the wall that is being considered for removal. If the house has any heating & cooling imbalance issues with the second floor, a second system is offered as a solution. The optimal time for this split system design is when the old, main heating & cooling unit needs replacement because one unit already has to be purchased anyway and adding a second system at this time is the cost efficient option.
Dampers cost less and work less effectively … the old adage of you get what you pay for.