The East just didn't have the same economic resources, nor the money to spend on football development. Big clubs also attract footballers to come play for them. I mean, really, look at the German National team. Other than Toni Kroos, basically none of their players were born in East Germany. Even he left an 'Eastern' club for Bayern at 16-17 to get better development.
They didn't have the same money, development and support of clubs in Western Germany. The East German national team wasn't as good as the Western counterpart, and the economics were the biggest cause.
As to where they are now, it's still related in development. The East has improved a lot, but it's hard to go from a poor developmental system to a strong one. You also don't have the same emphasis on youth development, and the economic investment. If someone in the East was going to invest in player development, they'd lose a lot of their players to the traditional clubs. Leipzig is able to develop and compete really only because they have the financial support and player pipeline of the RedBull apparatus. They could afford to put in the money and efforts to build the program from the ground up, and then go out and get young talent to come to their side. That doesn't mean it won't change over time, but the gap between Western Germany and Eastern Germany was significant, and it's still been a hard way back for the East.