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.
I'm not sure about Leipzig's income and the owners of this team but I know Leipzig had a perfect performance the last season and they got the third place in the table while because of the mistakes from both Dortmund and Bayern Munich, they could even race for the title with these two teams, but since Leipzig is going to play in the next champions league I think they should invest more for their team and improve themselves.
Player investment for the team is very important and for Leipzig it is something that must be done if you want to compete with other teams. So far they have managed to bring in several players such as Xavi Simons and also Lois Openda, but it is hoped that more players will come before the summer closes. After Nkunku joined Chelsea and also Gvardiol who reportedly reached an agreement with Manchester City this summer, I think they still have big funds to be able to bring in more players and maybe for the defender or midfielder positions there should be refreshment this time.