Well.....first of all we are just mortals here on this site. There are so many guys here with custom built rifles, dies, and experience at shooting fantastic groups at terrifically long range that it's almost embarassing to talk in terms of factory rifles and accuracy.
To answer your question with my experience level I would say it's a combination of both rifle and cartridge. The 30-378 hasn't gotten the rep for accuracy as I see often in the Rum. And a rifle with freebore probably won't shoot as good as a custom without it. However you have to consider yourself blessed to have a factory rifle that shoots as well as yours does. With a little fine tuning of your load charges and seating depth and runnout you might be able to get that gun down to a .5 moa rifle. If so and you can shoot 2" groups at 300 yds and 4-6" at 600 yds that gives you one heck of alot of hunting flexibility. But, the bottom line is do you have acces to that much range to practice and the time and money to get totally confident at those ranges. I'd say once you do and if you want to go farther you could be looking at custom rifles
and great scopes (and great expense) to take the game farther.