For what it is worth here is my take on that.
I would say it really depends how martial you want it to be or what is the purpose of the exercise. You do not have to do it one way, it depends what you want to get out of it.
My understanding of yokomen is that we want to hit the high value target on the side.
(Temples, ear, inferior maxillary and side of the neck) so we can really afford to make the strike becoming yokomen later in the strike.
So that our opponent does not know if it is shomen or yokomen straight away
If we go back to sword, striking with a strike equivalent to yokomen starting from the side, leaves our centre line totally open to a vertical cut.
That vertical cut is safe because he just have to do a normal step and he will have create enough angle
To add time to our strike to hit him.
And control our ams with his strike to the head, basically stopping our blow.
And with empty hand our opponent can reproduce all that by delivering a straight strike to our face whilst absorbing the Yokomen and using the same body movement as if ha had a sword
Now if you tart that yokomen with the point of the sword or the hand on your centre line.
The above counter his not that appealing anymore.
As well striking yokomen from the side will in 99.9 % of the case result in us striking outside our space. (ie over extending, unbalanced, having the shoulder in font of the hips)
This make tenchin back and grabbing the wrist a very viable option for our oppoenet, as if we try to subtract our hand or retaliate effectively, we will need to rebalance in some way.
So I would say it is easier to give ourselves away striking yokomen like that .
So I think it is quite convenient to help kinonogare or to help isolating the "ki" aspect of a given exercise.
If you strike yokomen starting from the top of the head, you much more likely to stay within your own space (or still in posture), which can make tenchin back and grabbing he wrist a task on the par with butterfly catching with bare hands.
I think that way of doing it is more convenient for the martial aspect. The opponent surrenders nothing to us, we have to take his balance, posture and ability to retaliate away from him
Thanx Phil. With my question I didn't mean to start a discussion on which way it was the correct way to do the Yokomenuchi, but the difference. As Ron said it does affect the technique, but I couldn't see how.
The way you put it out it is to me very clear. I can see by the way you pictured it how in one way Uke gives away part of his center from the beginning, while in the other way it is completely to Nage to take away the center.