I'll admit it's a strange feeling to finally have a real rival. Before Dortmund's recent emergence Bayern was the only consistent top team in Germany and Dortmund / Bremen / Schalke (+Stuttgart / Wolfsburg) all took turns challenging Bayern. But Dortmund's definitely there to stay now.
What really annoys me though, is that us Bayern-fans get called "Erfolgsfans" by our fellow Germans, I don't really know the English term... I think 'bandwagon fan' is closest. Which is odd because, for example I've been a Bayern fan before I even knew how succesful they were. Anyway, ever since Dortmund started winning things again millions of people suddenly remembered that they were lifelong Dortmund fans and started to ridicule Bayern and still dared to call us Erfolgsfans.... It's annoying but after last season I finally realized that it's just another way of showing respect
I think the adequate comparison for Dortmund would be, if Liverpool suddenly started winning and playing great football again...