People only need an elephant gun to hunt elephants.
This has to be one of the most over analyzed questions of all time.
Not saying "Don't ask questions, everyone should.
A well known hunter rifleman Randy Newberg I found on YouTube states it best.
He says when people ask him what's the best Gun for Elk, he tells them the gun your most comfortable with. So will a 30-30 kill and Elk...yes, I've seen as stated before deer drop dead in their tracks with a .22 from over 100 yards.
I'm not saying I'd take a 30-30 on an Elk hunt, but Newberg's point is well taken.
If you have a 25-06, or a 300 Weatherby and you've used it for years that you know what it can do, how it's going to buck when you shoot it, then that's your elk gun.
The knowledge you need to have is, how far do you feel confident shooting it. look to see what Bullets are recommended for taking an Elk, and they're is you Elk gun.
HaPpY ShOoTiNg
I honestly don't think there is going to be much of a difference unless you want to get a 26 inch barrel in a .300 Weatherby or RUM. I get 3000 feet second out of my 6.5 PRC with 156 Bergers Elite Hunters and Retumbo. Not really much different that 3100 fps with my 145s ELDXs in my .270s. No matter what you run in a .300 short mag running 180s those loads will deliver comparable energy at short distances, roughly catch up with it at 300 yards, and beat the socks off it after that. Caliber size alone is BS.
Now if you like Muzzlebrakes and burning powder, the .300 Weatherby and RUM will run anything into the 220 range just as flat and laser the 150s and 180s to the point that they of course are far and away your answer. For everything else on elk .257s (25-06 AI and Weatherby) with a fast twist barrel, the 6.5 PRC, the .270, and the 7mm Mag do everything your other 30s will do short range, beat their energy long range, and do it in flatter shooting, milder recoiling format.
Here is the your choice example with Hornady Max Loads:
You are going to roughly shooting the .300 Win Short Mag 180s Nosler Partition at 3000 fps, same as the Berger 156 Extremes
.300 WSM 3000 MV 3597 FP 300 Yards 2351 FP
6.5 PRC 3000 MV 3117 FP 300 Yards 2348 FPs
Of course the PRC is better with both wind and velocity maintenance for expansion at all ranges because of the huge BC difference.
Your 6.5 PRC catches the WSM in Energy at 300 yards and smokes it after that. So yeah the your 6.5 is arguably a better elk cartridge than the .300 Win after 300 yards. You can play with your BC loads with heavier .30s but the loss in velocity puts the results the same. Your .300 Win Mag with the same bullet can hang to about 400 yards and maybe a bit better with heavier bullets.
There are always good reasons to buy another gun but don't handicap yourself with a lesser option because of the theory that bore diameter matters.
You really want to blow some minds look at what the 25-06 AI or especially the .257 Weatherby will do with a 1:7 twist and the new 133 Berger Extremes. It takes another 100 to fully catch up in the energy department but its numbers are comparable to start and when you can send that bullet out at 3200-3300 fps it just completely smokes anything up to a .300 Weatherby in the 30s while giving you a 500 yard laser.
Get you whatever gun you like and it will do the job but so will your PRC and just don't get caught in the trap of thinking the something like the .300 WSM is a better elk gun than what you have. The numbers would argue the opposite in fact.
As far as the 30-06 goes the .270 or PRC smokes it across the board. Its obvious that a 145 ELDX or even 150 .270 Partition will very quickly outperform the 30-06 in a 150, but people don't realize that a 130 is a better choice in a .270 over a 30-06 150, and that the 145s or 150s will quickly catch any energy advantage of the 180s have. There is almost no advantage at all over the 156s even short range vs. your PRC with the 180s in the 30-06.
As I indicated you can use higher BC bullets in the .30s you are looking at to try to keep up on energy but at the expense of initial velocity loss and bullet drop at hunting ranges and that only buys a few yards of competiveness for these .30s.