Jack Nicklaus during his prime. That would be his entire career. He seem to hold the putter clubface high and facing the hole at the end of the stroke.
Would that be vertical hinging?

I would say that Jack was a "hitter" with his putting stroke and used angle hinging, the putter face was across his plane line. But I would like others to chime in on this one.
Not many horizontal hinges out there with the good putter these days but maybe I'm missing a few. Angle hinging to me makes the most sense but I'm searching right now too!
Vertical hinging is a manipulation of the putter head and to me not very reliable.
Just the ramblings of a dressed up caddy with his brains beat out.

In a putting stroke angled and vertical hinge become nearly identical.
Practice along a 2x4 and keep the heel of the putter against and at 90 degree angle to the 2x4.

I tried to go from a Ping Anser to a face balanced putter a few years ago. That was a big failure. I like to putt with forward press. A face balanced putter will then flip open in the back swing and flip closed in the follow thru. So I had big problems keeping the club face stable through impact. But it depends on your stroke. If you simply let the putter hand down from your hands and swing it from there it probably works OK. Also, you get a bigger sweet spot and perhaps a nice gear effect when the COG is far behind the club face.

A Ping Anser type of putter is very different. It has a more neutral weight distribution and is also much lighter overall, so you can basically use it as an extension of your hands.

Someone ought to make a 360* balanced putter - one that didn't have any face angle bias at all but left everything to the player's hands. A putter where the moi center, the cog center and the sweet spot were all in the same point. Then the clubface would obey your hands without resistance regardless of your stroke.

BerntR
Remember the Sergio Garcia practice putter? it was a shaft with a brass ball on the end that was the size of a golf ball.
Heck, I may even have one in my basement.

No I haven't seen that one. A brass ball as the club head?

I just looked one up on ebay. It is called the Putterball.
I cannot imagine they are produced any longer, but one good thing about them was the ability to practice a lot of forward shaft lean.