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.
Leipzig gets me excited quite often because everyone would think that they use their RedBull billions to elevate the club to the top of the table in no time, but they are not doing that. Could they do it? Well, I still think it is hard to believe that they became so dominant in a sport like the Formula 1 when they are competing with all those car manufacturers, so they could probably get RB Leipzig jump-started even more with their cash, but they don't. Neverthless, they are one of the toughest competitors for Bayern Munich without making these billionaire club moves. They received a lot of disrespect from the public, but since they never abused their financial superiority and yet played successful they became one of my favorite German teams.