The BOP model is focused on taking a single product or service and finding ways to make it cheap enough to offer to a larger, poorer, market. This is why I think it's essentially about commodification.
The Long Tail, on the other hand, is about nicheification. Rather than finding ways to create an even lower lowest common denominator, the Long Tail is about finding economically efficient ways to capitalize on the infinite diversity of taste and demand that has heretofore been overshadowed by mass markets. The millions who find themselves in the tail in some aspect of their life (and that includes all of us) are no poorer than those in the head. Indeed, they are often drawn down the tail by their refined taste, in pursuit of qualities that are not afforded by one-size-fits-all. And they are often willing to pay a premium for those goods and services that suit them better. The Long Tail is, indeed, the very opposite of commodification.
So the Long Tail is made up of millions of niches. The Bottom of the Pyramid is made up of mass markets made even more mass. Both lower costs to reach more people, but they do so in different ways for different reasons. They're complimentary forces, but fundamentally different in their approach and aims.