The darker grout will make the tile pattern more pronounced. Because your counters seem to have a strong pattern / prominent veining, my preference would be the lighter grout so that the backsplash doesn’t compete with the counters. It might help if you post another picture that shows more of your counters.

Accent tiles in the hood area are not "in fashion" right now. Just an fyi.

Also, how do you plan to separate the 2 patterns? A frame with pencil liner? Personally I don't like when one cut pattern butts up to another cut pattern, without a border/frame between them.

For the white tile I would match the grout exactly to the backsplash and probably use the same white for the hexagons. You are going to have a lot of pattern going with veins/stripes for the counters and hexagons and rectangles for the backsplash