A square hole, or a hole that has a Taper to match ojive??
I think you are trying to contrast an edge contact versus a conformal contact surface?
Both can work equally well if the operator keeps the contact forces managed equally well.
In inspection or metrology labs, we would call these tools comparative since the edges on the Hornady style still have a break or chamfer. So they cannot meet the strict definition of a cutting plane at a hole diameter when being used on curved ogive shapes or conical case shoulders.
The friction and contract stress of both styles means you will need to "standardize" how much force you put on them. An area contact will typically be more repeatable than a line contact when inspecting a curved bullet surface, but with that said it doesn't matter in this context. The method is supposed to be comparative, not absolute, and for practical internal ballistics that is better than required when done properly.
Tool set ups that use low friction indicators, with controlled spring forces, tend to be better than hand operated ones because the contact forces are controlled better. That is not to say you can't do this by hand with a 6" caliper and the Hornady style tools, but you must be careful to get good results.
You can learn to use either style tool with some careful attention and dexterity. When we teach new techs, we hand them the GO-Gage or a steel dummy reference bullet to practice with till they gain proficiency and understand the contact pressure and friction issues. Once they have the hang of the tools on steel, we let them loose on brass and bullets.
If you use a "standardized" bullet that you keep for set-up tooling as a reference before every session, and zero your tools against it... you will start to get better results. Same thing applies to shoulder datum tools being zeroed against a Go-gage. YMMV