Thanks, Sennahoj!
Sennahoj got it right, OC.
With best play Black wins by 1; with best play White wins by 1.
When the move at C gained 1 point, each player was indifferent between playing at A or B. When the move at C gained 0.5 point, neither player wanted to get it. Black took the sente at A and then the gote at B, leaving White with C. White took the gote at B, leaving Black the sente at A (which gained nothing) and C. In this case the move at C gains 1.5 points. Does this mean that each player wants to get it? Well, White does, anyway.
White plays the reverse sente at A, yielding B to Black, and then gets C. If White took B first, then Black would take the sente at A and then get C, as in the previous case.
In all three cases Black can get the optimal result by taking the sente at A. In fact, as I now know, if there are no kos involved, when the choice is between a simple gote and a simple sente with a threat larger than the gote, it is not wrong to choose the sente, regardless of what else is on the board.
By not wrong I mean that taking the sente instead of the gote will lead to the optimal result, given best play otherwise.
But way back when I was first studying these things, I came to believe that Black should take the gote in this and similar situations.
Below I have amended Sennahoj's SGF file to make Black taking the gote the main line, and I have added White's mistake of taking the gote as a variation.
The point of Black taking B first is that it gives White the chance to make the suboptimal response of taking A, which gives C to Black. In that case Black wins by 2 instead of 1. Yes, the reverse sente at A gains more than the gote at C, but C is the last play. White wants to get it as long as it gains more than half of what A gains.
With C so large, this example is really about who gets C.
White to play gets it by taking the reverse sente at A. When Black plays first, White can always get C with correct play, but Black can lay a trap by playing B first, tempting White to make the largest play at A and letting Black get C.