Leipzig are also not so differen than Dortmund when it comes to vision. Otherwise as you said Leipzig are normally a rich team that can be quite convincing to sign better names by offering more money. It won't be easy to compete with Bayern Munich regularly anyway of course. Because it will take them a quite much time to build as good squad as Bayern Munich's. Besides there will be some time needed to have full chemistry among the players as well. Besides it doesn't end there either.

Management of a team is the most important thing for successes. If the owners don't have a good understanding of management then it is still quite difficult to achieve big things.