By dumbing down Khan, making him just focused on revenge, you loose a lot of his threat, his menace.
Well, I personally think "dumbing down" is a bit of a skewed description and that Khan's progression to an Ahab-analogue was one of TWOK's deftest touches. In part because it was unexpected and in part because it provided a way to reintroduce him that didn't make Kirk's original decision to maroon him on Ceti Alpha 5 look completely nuts. (Only moderately nuts.
For my money the revenge motive also actually made him more interesting, not less, than his previous Oriental Despot power-madness; and it also made him more believably flawed and his errors in judgment explicable.
(Conversely, STiD Khan had no similar excuse for having loaded the people he supposedly cares about into seventy-two pieces of explosive ordnance, just for example. And his Emperor Palpatine-like "no ship should go down without her Captain" line is motiveless B-villain malice, of much the same type that Marcus is suddenly afflicted with at a certain point in the story -- rather at odds, one might say, with the nutty but still patriotic "bombs away" mentality he'd hitherto displayed. I like the way Cumberbatch sells Khan at other points but I don't think this in any way diminishes or eclipses what Montalban did with the character, not by a long shot.)