Again we come back to the definition of what is a good layback, what is the point of this element?
Why has this spin been required (for ladies) for so many decades? What value does it possess?
My guess is that it's a combination of two reasons:
1) Many women are able to achieve beautiful whole-body curves through back and free leg that enhance the aesthetic value of their programs, in ways that are considered traditionally feminine, and the ISU wanted to encourage all female skaters to develop that skill as much as possible.
2) Aesthetics aside, the ability to center a spin with the upper body off axis is a marker of technical skill worth rewarding. Note that the SP requirement has long been "layback or sideways leaning spin" and has not dictated the minimum acceptable position in any more detail than that.
From a purely aesthetic point of view, one could say that any attractive position should be rewarded, and any unattractive position should be avoided by skaters and penalized when executed.
"Attractive" is often in the eyes of the beholder. There are certain basic principles of aesthetics that most eyes will agree with, such as the "classic" attitude position with deep back arch, but different skaters have different body types so they're not all going to be able to create the exact same shapes with their body. Some observers will dislike anything that deviates from the classic position in certain directions (leg too low, back not arched enough, back arched too much, free leg not bent, asymmetrical back position, etc.) while others will enjoy well-performed variations.
From an acrobatic point of view, flexibility could be valued for its own sake. In general more flexibility tends to be associated with the ability to achieve greater aesthetic appeal, but sometimes extreme flexibility can look like contortion and turn off some viewers. Also rewarding certain positions just for being achieved will encourage skaters to attempt them whether they have enough flexibility to look good or not, so we see a lot of bare-minimum-acceptable, or failed, haircutters and Biellmanns by not-so-flexible skaters that may or may not give them an extra level but that detract from the aesthetic appeal.
From a technical point of view, a "good" layback is one that achieves at least a minimum acceptable body position with good centering, good speed, many revolutions. Those would all be reflected in the GOE.
Being able to achieve both the backward and sideways positions, being able to change edge while in the laid-back position, and being able to arch the upper body backward at all in a backspin all add to the difficulty, so they can be rewarded as features.
Looking at these two male laybacks, I agree that Ward shows more flexibility and a more aesthetically appealing curved shape -- which some gender bigots might consider too "feminine" for a man but as far as I'm concerned it's a plus. The spin is well centered and it has about 10 revolutions, so well over the 6+ expected in a senior freeskate. But it is kind of slow. So under the current GOE guidelines I'd go with +1 but could understand +2.
Takahashi's is faster with more revolutions, enough for extra credit on each but not up to the level of the top female laybackers; the position is not unattractive IMO but nothing special, and the centering is mostly good but there is a slight amount of travel. So again I would go with +1 but could understand +2.
However, he did more than a basic layback here. What I'm most impressed with from a technical point of view is the edge change. That is sooo difficult in that position, and he made it look effortless on this occasion. He also had the change from sideways to backward. So that's two obvious features -- I'm guessing he also got credit for 8 revs in the same position and for acceleration? Even without those latter features, it was still a more difficult technical feat than Ward's, so a higher level and a similar GOE for different reasons seems appropriate to me.
So if there were a fixed base mark for "layback" and no levels, I would want to reward Takahashi for the difficulty in that edge change in the GOE. Either way, I think that spin deserves a higher score than Ward's.