An acquaintance of mine actually works for Otto and he told me several things. First of all, in the heads of many people at that company the catalogue is still the main driver of revenue. Online is more or less an afterthought. This is also reflected in their average customer who is older and less educated than the average Amazon customer. Secondly, their IT is ancient by Silicon Valley standards. Orders, for instance, are allegedly only processed once at night by batch job, because their infrastructure doesn't support anything else.
All in all, my money is on Amazon and Zalando (basically an Amazon clone supported by the infamous Samwer brothers) who will soon run circles around Otto if they don't catch up fast which isn't an easy thing to do with a slow behemoth of a company like that.