Just to clarify, however, it's my understanding that it should be a similar or more flavorful beer that will use the re-pitched yeast. You can step the beer up on a used yeast cake, but can't go the other direction.
For example you could reuse an APA yeast cake to brew an Imperial IPA or an Irish Stout (just examples, not recommendations), but couldn't go the other way with it without affecting flavor.
Also keep in mind there is a limit to how many generations of yeast you can produce before genetic mutations begin to produce off flavors in the beer. You would probably get tired of re-using the same yeast long before this happened, but it is a possibility. Many yeasts can be re-pitched up to 10x, but I've heard of some losing viability and genetic stability as low as 5x.