Most of the tongs I've seen tend to be fairly straightforward in design: heavy boss at the pivot, straight reins tapering gently away from the boss, and whatever shape the business end happens to be. Basically like this:

I've recently encountered tongs with a pretty hefty shoulder behind the boss, like the ones being made in this video or the ones in this image. 

I'm curious what the rationale is behind this alternate design. Is this just a farrier thing?

I've watched videos on YouTube showing 'blacksmithing championships' where they forge horseshoes and tongs just like the ones you linked to. The whole time I'm watching I'm wondering the same thing as you. I've never figured out why they are shaped like that but I have debated on trying to make some just to have a pair.

Some of the farriers' manufactured tongs had that appearance, so it became a sort of style for horseshoers. It is not necessary, although it looks "keen." In fact the traditional Japanese tongs eliminate the "third shoulder" leading into the reins altogether. Their first shoulder demarcates the jaw base; the second shoulder is the diagonal one which flattens the boss. From there, the Japanese smiths forge a taper in width going into the rein. Not a shoulder.

Post Script. To each his own, but I like my reins to be parallel. On my tongs, I put a mild curve behind the "third shoulder" and fine tune the two reins hot so they are parallel and comfortable to the hand.

Like these?

Yes, as pictured.

8 minutes ago, Frank Turley said:

Yes, as pictured.

Interesting; thanks, Frank. 

I have a tong making video where Bill Epps shows three different approaches to making the blank.  The "shouldered" one he called a "Champion style" tong after the Champion company.  The starting stock is symmetrical (square or round) and it's fullered twice along the same side.  The end most fuller is the jaw bend, the other fuller is the handle bend at the boss.  Once those fullers are in, the area between them is forged perpendicular to the fullers to draw out the boss and allow the jaws to overlap.

Bill Epps said the Champions were his favorite style because he felt they were stronger and faster to make.

One thing that I noticed about them is that the area behind the boss isn't flanked by angling handles.  Hanging the tongs from a single rail would leave the handles pointing straight down.  On some of the angling handles, the rail would spread the handles which takes up more room on the rack.

I also noticed that the more right angled handles would tend to make it less difficult to hold something with your hand right next to the boss.  The lack of pinch points is always appreciated in a hand tool.

I've been meaning to try to make a set to see if they're any easier/stronger/better.  I think the square shoulder looks nice and professional.

1 minute ago, rockstar.esq said:

I have a tong making video where Bill Epps shows three different approaches to making the blank. 

Is that this video? Looks like a sample from his "Making Tongs with Bill Epps" DVD.

JHCC,  Yes, that's the one.