I think King of the Hill is much closer to normal Chess than 3check. Before the end-game the center is usually not accessible to Kings, not even when they are suicidal. An if you get ahead enough in the middle game that the end-game would be won in normal Chess (e.g. a minor ahead), you will usually be able to force your King to the center as well.
With 3check you really have to be well aware of how much the first and second check are worth, compared to material. E.g. is it a good deal to sac a minor for the second check, or even a Rook? Is the first check worth a minor, or not even a Pawn?
I was not particularly interested in chess variants apart from Chess 960 ( I thought that they are not really chess ). However watching live games at a site a high rated king of the hill game came up and I found it interesting ( this is: the side which can put its king in the center wins, in the case of three checks the side which hits three checks sooner, wins ).
I started playing and to my surprise I'm much better in king of the hill than three checks. I have known for a long time that I'm worse at quick time controls and that gambits are not for me, but it comes to me as a surprise why I'm almost 200 points better in one variant than an other.
I wonder what skills king of the hill requires that are different from three checks.