Mine is a Shilen DGA 338. Bought the barreled action, sent to Mcmillen, all up about $1300. Worked up a load that consistently shoots 3/4 moa, absolutely HATES barnes x-bullets.
As to the 338, can be loaded up down very successfully. Loads for a family member launch 250 grainers at around 2100fps for fla whitetails, he loves it. This will probably start a firestorm or two, but NONE of the other cartridges that you mention will ever be loaded to do what the 338 will, but it can be brought down to their level, IMHO.
