I see that John Fairbairn has beaten me to the punch. I have a somewhat different take, but I see from his note that the pros are much more likely to choose to make a White wall when White has a stone on the left than when Black does.
In the examples shown, with sanrensei of different colors on the left. I would certainly build a wall to work with them if they were White, but would jump into the 3-3 if they were Black. The point is, as I said, the wall would work with the sanrensei if they were the same color. However, that is not so if they are opposite colors (obviously). Then the wall might (?!) support an invasion, but the sanrensei is invadable, anyway, and the extra value from the wall is dubious.
As for countering influence, you might end up with a wall if you make a reducing play, but the reduction is logically prior, the wall is the result. But suppose that Black started, not with sanrensei, but with a wall. Then jumping into the corner and letting Black build another wall is dubious. Then is the time to counter wall with wall, influence with influence. (BTW, I think of influence as a Western term, not the same as atsumi or gaisei or seiryoku, etc.)
That said, I think that there is a misunderstanding on the part of many amateurs, particularly in the West, about the ability of single stones to counter or "kill" influence. I think that it is instructive to look at some of the ancient games of the 18th and early 19th centuries. Players then were more territory oriented than now, yet how often were they willing to make walls that seem to be ineffective -- and, indeed, often to do nothing obvious with them. Most peculiar, mama!
But that is a different question from the one posed by these examples. Here I think that a wall would not be much help against an opposing sanrensei.
As for the question about the opponent's move being my move, the two walls are not comparable. Black's wall is further from the sanrensei, and in addition, the 6-3 stone threatens to run.
I'm using Safari.
. White's influence doesn't neutralize black's sanrensei, but it does affect direction of play. Fighting in the center should be good for white now, because he has supporting stones.
Well, I'll fix it soon. In the meantime I guess you'll have to play it out, sorry. My two positions were comparing white G14 next vs N16 next.