Both techniques (TS and GA) are often associated as they are complementary and can achieve spots with a very high degree of satisfaction. for example the GA was hybridised with Tabou Search which tries to repair infeasibilities in the solution.
For more details about this subject i suggest you to see links and attached files in topics.
-Personnel Scheduling: Comparative Study of Backtracking ...
Personal schedule can be solved by hybrid metaheuristics using some local search operators. Those are needed to prevent find local optimal solutions instead of global ones.
These are two different types of metaheuristics. Tabu search is a s-metaheuristic (point-based) that iteratively modifies a single solution to a problem. GA is a p-metaheuristic (population-based) that iteratively modified more than one solution to a problem. Each has their won distinct behavior in solving a problem. It would be difficult, with limited information, to say which is better. I would search specifically for heuristics that were applied to the problem you have to solve.