I have a .300RUM and have shot a .30/378wby.
If it's another "level" above the .300RUM, then the .30/06 is another "level" above the .308 (hint, it aint!)
In fact, depending on barrel, ammo, and atmospheric conditions, it's a "wash" in many instances.
The rifle I shot was a factory Weatherby MkV Super-something. Heavy, fluted barrel, stainless steel w/decent synthetic stock and muzzle brake. Had something like a 4-15x Swarovski or NightForce scope on it.
The individual was at a public range on state property trying to sight it in. He couldn't.
I offered to help him.
1. I removed bolt and "bore sighted" it at 25yds. The shop who sold it to him had done so with a collimater/bore scope and due to height of scope over bore was "way, way off" vertically.
He hadn't helped by running the windage all the way to the left trying to center the group.
2. After firing one shot and correcting it at 25yds, I moved it to 100yds. One shot and then moved the scope to get +2.5" high at 100yds. Then fired 3 more rounds to verify. Got a nice 1.1" group centered and backed away from bench and allowed "OWNER" to shoot it. He missed the 18" tall x 24" wide target 3 times !!!! (flinch !!!!!). (shooting from an "Outers" gun rest with a pad against shoulder.
I shrugged my shoulders and suggested he take the rifle back and trade it for a Vanguard in .243wcf. He did !!! Rifle was back in the rack the next week....
He'd shot a box and 1/2 before my "intervention", and returned the rifle with 6 rds. Ammo was 180gr w/A-frame bullets.... IRRC. Cost him almost $100.00 a box.
I didn't think the rifle "kicked" all that bad. Muzzle blast was very significant. Not quite a .50BMG, but getting there.
For 99.97% of hunters and hunting, it's "over the top". For some target applications, it's great. If I had one, I'd be feeding it what I feed my .300RUM, WC-860, or WC-872.
But, I only occasionally take my .300RUM to the range, and have only used it twice to hunt with in the last two years, hadn't hunted with it before then since 2006....
But, where I was hunting on an airport, it was the "cats meow".... The 180gr Hornady SST "popped" a doe like a ripe tomato at a lased 387yds.... with only ~4" of hold-over. Load was 100.5g of Retumbo for a chrono'd 3,360fps @ 30'. (26" bbl w/0.375" freebore).
On deer, the .300RUM doesn't do anything my .257wby Vanguard doesn't. The "little" Weatherby kicks and barks about like a .270, but shoots as flat as a .220Swift. What's not to like????