I think in the long-run, it'll be price.
Sure, in the short-term, Amazon can do what they do and undercut on price, but in the modern age, Wal-Mart has pretty much figured out the optimal model of inventory storage/distribution and the model of keeping inventory on-hand and having customers come to them enables them to do this at an incredibly large scale and at razor-thin margins. Yet they are still margins.
As we have seen before, delivering products at that scale and selection via delivery is extraordinarily challenging to do profitably. Amazon can do a lot of things, but one thing I don't think they will ever be able to do is bring products to peoples' doors at a cheaper price than Wal-Mart can store inventory in large stores and distribute to customers who come to them. There are just too many complexities around the delivery/customer service/quality control processes to make the economics work out.