These sound like quite distinct promises to me, and the rhetorical effect is clearly very different; but if poverty is defined in purely relative terms (as both the UN and EU do), are they effectively promising the same thing? In fact, couldn't one "eliminate poverty" simply by reducing the country's median income, and leaving the actual circumstances of the poor unchanged? Statistics aren't my strong point, but I find this idea kind of bothersome.
In fact, I'm wondering whether Robert Mugabe isn't eliminating poverty in Zimbabwe even as I write. After all, he's managed to reduce the median level of income dramatically, thus (presumably) bringing many of his poorer citizens above the 50%-of-median-income level used by the UN in their definition of "poor". The fact that he and his cronies live in luxury won't skew the figures either, since it's a median rather than a mean figure.