As a (poor) Go player, linear growth rather than exponential sounds right to me. In chess, every piece you take is a piece your opponent no longer has - death is permanent. In Go, if you lose a piece, you can hope to make up for it later. You're down one piece, but it's not like losing a bishop - it can be replaced*. In Go, poorer play doesn't necessarily lead to a collapse of a figure and its complete capture, but more usually leads to simply a smaller figure. Big figures, equivalent in value to a queen, say, are almost always alive (either because they're big enough to have 2 eyes in their own right or because they can connect outwards) and can't be lost.

* I ignore pawns advancing to the last rank; the promotion rule can matter a lot in chess, but it doesn't pervasively affect the whole game and rise inexorably out of the game mechanics.