Considering how much worldwide poverty has dropped over the past few decades, I think it's safe to say that increasing the size of the worldwide economic pie is far more important than redistributing it, at least with respect to third world countries.
We've never tried redistributing it, so we wouldn't know.
Oh really?
Even if we accept that every one of those countries made a good faith effort to democratize their economies (which... umm...), none of them falls under the category of "rich country compensating poor countries for decades of exploitation, plus giving them a fair shake in the future".
We've given trillions of dollars in foreign aid to those poor countries over the decades. The real issue is that there aren't sufficient incentives to invest in those areas due to a lack of human capital. You seem to act as if prosperity is the natural state and poverty is caused solely/mainly by exploitation, whereas in reality, poverty is the natural condition and only through a combination of capitalism and human capital development can a nation be lifted out of development. The West has already made this leap, and East Asia is well on its way. Here's the thing: why do you think companies are investing so much to build factories in China/India (and we see them as taking jobs) but not Africa? Because a lot of the continent doesn't have the necessary skilled workforce, infrastructure, etc. to attract capital and investment. That's the thing that really needs to be changed, which involves some foreign aid but also major structural reform in African states.