In Japan, we don't use the technical terms like Sente and Gote in a handicap game. Instead, we use Uwate(more skillful player) for a handicap giver and Shitate(less skillful player) for a handicap taker. And, Uwate, a handicap giver, always moves first in handicap games.
The color of Uwate is White and that of Shitate is Black. Why? I think this is due to the conveneience of printing industry in Japan. Looking at shogi books in Japan, the lower side of a diagram of a handicap shogi position is always Shitate(black). The player who needs to read such book is definitely novices/begenners and it is easier to understand the position if the lower side of the diagram is Shitate(Black) rather than Uwate(White). I think this is true for Igo handicap games. White(a handicap giver) drops first there.