Every gun is different with its own personality, same as people.
But as a rule many Handi's will shoot very well out of the box, most others can be made to do the same with minimal (do at home) work.
Like most of the guys here I have a handi or two that will shoot 1/2MOA @ 100.
Others that struggle to get 2". It depends of caliber too. The ones I have that are 2" guns is all I need from them. One of my 45-70s that's all it will do.
My 500S&W is about a 1.5" gun with the hand loads I have tried so far. My buddies 500, (ONE digit SN different) will shoot almost one hole, easily keep them touching, with the same hand loads.
Buy one of these in a Ultra, in any/all of these calibers. There is a much better chance you'll get a good shooter that looks better too!!
Good luck,
CW