If you have anatomical feature X, and someone pushes a button to increase the utility of all people having feature X

This assumes some correlation between anatomical feature X and a term in a person's utility function.

Based on your comment and this exchange, it's not clear to anyone what exactly are we talking about (my first question was "What do you mean?" for a reason). The conflict I took as the topic of the conversation is generally the direction of change in balance of influence (i.e. status) between partners or potential partners in a relationship from the default established by social status quo.

If you reason in CDT style, then the only effect of increasing your own influence is improvement of your experience in your present relationship. (Incidentally, I don't see how your sex is relevant to the character of this activity, the salient category seems to be simply your own person.) This way of thinking seems to explain your discussion in this thread best (correct me if you were in fact assuming something else).

Alternatively, if we are talking about influencing the social status quo, then from the (narrow) point of view of any potential heterosexual relationship, you win from the improvement in relevant aspects of background status of your own sex. It would be obvious that the result of such shift is beneficial overall only if you focus primarily on egoistic value effects of its consequences, ignoring the effect lowered background status has on all of women (which is huge scope). This is essentially the sense which I assumed in making this comment. (This works the other way as well, i.e. the effect worsened relationship experience would have on all of men.)

The reason the first looks like the second to me is that from TDT perspective even the personal decisions you make in influencing the course of your own relationship, without intentionally meddling with the global status war, have global effects through decisions made by other people for similar reasons. If you decide to pursue greater influence in your own relationship, this allows you to infer that other people would behave similarly, which makes for a greater damage to opposite sex's values than just your partner's.

So even if we make the reasonable assumption that you hold your own immediate preferences in greater value than other people's, and so you'd be inclined to bargain in your own direction, the combination of possibly greater marginal value of improvement for the other sex with nontrivial scope of the decision makes it non-obvious.

The rest rests on the factual and moral questions of who gets how much greater marginal benefit from shifts in the current default status quo influence. There seem to be convincing arguments for both sexes.