We investigated the sensitivities of atom interferometers in the usual fringe-scanning method (FSM) versus the fringe-locking method (FLM). The theoretical analysis shows that for typical noises in atom interferometers, the FSM will degrade the sensitivity while the FLM does not. The sensitivity-improvement factor of the FLM over the FSM depends on the type of noises, which is validated by numerical simulations. The detailed quantitative analysis on this fundamental issue is presented, and our analysis is readily extendable to other kinds of noises as well as other fringe shapes in addition to a cosine one.