You're comparing not apples and oranges, but rather poker and blackjack. The writers use all of the same tools, but the rules under which they must operate are VERY different.
Howard's stuff is clearly pulp influenced (no big surprise there!), which tended towards excruciatingly descriptive details on the surroundings and violence. Protagonists are monolithic, unchanging, iconic ideals, their worldviews very black and white, even if they walk along the grey boundaries. Their conflicts are easily defined. The heroes are to be admired and emulated...maybe even worshipped. We identify with them because we wish we could BE them.
Meanwhile Lackey and the others' work show more modern influences, especially the snarky Pratchett. They're more interested in character development and internal states than earlier writers. Cherryh spends equal time writing sci fi and fantasy, and it shows. Ditto Donaldson. The characters are often regular people thrust into unusual situations. We identify with them because we ARE them. Their worldviews are all shades of grey, their conflicts involve sliding scales of morality.