Krieger and Criterion are NOT the same company or owned by the same people. This is a myth. The confusion is that at one time (a long time ago), Criterion opened shop in the same building as Krieger, but as a separate business. This was aparently an big industrial complex with multiple clients. Both companies have since moved to separate buildings.
I will say that Criterion has prided themselves at making drop-in barrels to USGI drawings using ex-US government rifling machines. Their barrels index without work and generally all you need to do is ream for headspace (unless you buy the chrome-lined versions). Their chromed government profile is a perfect match to USGI drawings and is service rifle match legal in the USA. They are less expensive than Krieger barrels and whether one is superior to another is a matter of opinion since no two barrels are exactly alike from any manufacturer.
Krieger leaves their barrels under-indexed and the shoulders have to be machined to index - this is to allow for receivers that are out of spec. Their barrels are cut rifled, a more expensive process. There is much debate if cut is truly superior to button rifling, but GI barrels were button rifled FWIW.
I personally prefer Criterion barrels for the kinds of builds I do, but I'm not a super-heavy match barrel kind of guy.