Which barrel typically has more accuracy potential, a cold hammer forged one or a button rifled one. Also which type would tend to hold POI better between temperature extremes.

Thats a easy one. Button rifled. FNMauser

I seriously doubt that you could tell the difference. Most aftermarket barrels are button rifled if that helps.

Some of the finest barrels are still cut rifeled, the one that I am thinking of offhand is Kreiger. About as fine a barrel as you can find anywhere.

A fairly academic question with no real answer IMHO.

Look at the benchrest set, they use a variety of brands and styles with a variety of results and even major variations between barrels from the same makers. Some barrels just happen to be sweet in a given action with a given load.

IMHO the smith that does the job will have more effect than could be attributed to a particular type of rifling.

I have NEVER seen a hammered barrel used in competitive benchrest. Only the finest pulled button or cut barrels are capable of the accuracy required now days. Then a good BR smith has to do the rest.

rws,
and then the benchresters may through 20 of those away before they settle on one...

Possible, some evidently do. If they want to end up at the head of the pack, they do whatever they think will give them an edge. Most of the shooters don't go to that extreme, buy one or two each season and hope they shoot real good. But buying a hammer forged barrel is not one of the proven methods of shooting at a competitive level.