Which projections you favor?

[mapnerd2022]

The Cylindrical Stereographic is much better. The Cylindrical Equidistant flattens the temperate and polar regions too much.

[PeteD]

But then the cylindrical stereographic has greater areal distortion. It's all swings and roundabouts.

[mapnerd2022]

But then it has better shapes than the Mercator.

[Atarimaster]

But then it has better shapes than the Mercator.

I’m confused here. Better shapes than a conformal projection?
Talking about local shapes, that’s not possible.
Talking about global shapes … well, of course, the increasing areal inflation towards the poles make Alaska or most notably Greenland look different than on a globe. But still the shapes are better in my opinion than on any cylindrical stereographic projection, even when we’re talking about the “look and feel” (or the “Urbildähnlichkeit”, as Wagner called it) as opposed to metric properties.
So, could you please elaborate on that?

[mapnerd2022]

Although compromise projections distort all shapes, larger shapes are less distorted than on conformal projections.

[mapnerd2022]

Or global shapes as you called them.

[Milo]

Oops, sorry I'm late, I missed this post before:

A while back, I was interested in trying to figure out which pseudocylindrical equal-area projection would have the "least" angle distortion, by a minimax criterion.

How does this minimax criterion differ from the one that gives the circular Hammer?

It doesn't, it's the same criterion. The difference is that the circular Hammer projection isn't a pseudocylindrical projection.

[mapnerd2022]

Of course, because it lacks constant scale along the meridians.

[Milo]

Of course, because it lacks constant scale along the meridians.

Pseudocylindrical projections don't have constant scale along the meridians.

[mapnerd2022]

They don't?