The rate of growth is indeed faster in developing countries than developed countries. This is to be expected given that they recently started at a lower level of development.

In rich countries, however, inequality has trended up, while in many developing countries it has trended downwards. But even that is a mixed bag.

In the largest developing economies (China and India), inequality is increasing, so the rich are getting richer there faster than the poor are getting richer. Of course, the jump for many people from utter poverty to having even the basics is a massive one.

It gets more complicated though. In Latin America, inequality is generally decreasing despite relatively high growth.

In the developed world, inequality has grown as those with investments and/or skills tied to global growth have seen their wealth rise, while people lacking either of those have seen wealth decline. This phenomenon and the disinvestment in public infrastructure that has accompanied it, has been credited with the recent populist swing in politics in the developed world.