In the strictest sense, I think they mean the same thing; namely, those whom God has saved, He will preserve and not allow to fall away.
It is legitimate to ask, Are those two ways of speaking equally useful? I think the question comes out of a fear that if you say, “Once saved, always saved,” it will sound like a carte blanche to go live any way you like. This expression can sound antinomian because it could be interpreted as saying, “God is stuck with me now that I am saved, so I can live the way I want because He still has to save me.” That is not what most of the original “once saved, always saved” people meant, but I can see how that is a concern and a potential danger.
On the other hand, the perseverance of the saints stresses that we live as saints perseveringly—we go on living as saints, pursuing holiness, and living by faith. As a matter of Christian living, the doctrine that we must persevere is more helpful. At the same time, we do not want to turn our responsibility to persevere into a righteousness based on works either. We always want to link our perseverance to our confidence in God’s preservation.