Well "that much better" would be a mater of opinion.
The 6.5 G picks up about 16-20 FPS per inch from 20 to 24 inches. So "that much" is a prospective.
For my way of thinking, 80 FPS over the velocity of the 20 inch barrel is something I hold up against what I call "real world use". I ask myself, 'what animal, at what range, would an impact velocity with a .264" diameter bullets of 123 gains at impact velocity of (for example) 1800 FPS be inadequate, but 1880 would be fine'?
To me it means little of nothing.
Now when I chronographed the difference of the 6.5 Grendels with 16" barrels, and compare them to those with 22 and 24 inch barrels, I saw a far larger difference. About 200 to 250 FPS.
In the 16 inch guns I have seen a bit more velocity with the 6.8SPC with 115 and 120 grain bullets then I see with the 6.5G with bullets of similar weights, weights up to 125 grains. That's why I see the 6.8 as more of the "carbine round" and the 6.5 as the "rifle round".
This is just one man's experience. All loads are not known to me, with all bullets, in every barrel length, so others may see things a bit differently.
As I said in the above post, I have seen a bit more dramatic effect with the 6.8 then the 6.5 in killing game from about 15 yards to about 250 yards. From 250 to around 300 they seem equal. Past 300 the Grendel starts to walk away from the 6.8. Neither is vastly superior, and both are close to intermediate range rounds.
So you will not be disappointing at all with a 6.5G, but just understand it is not a 30-06 or 7MM Mag and can't ever be.
Personally I only shoot to 500 meters at any animal. So I see no huge real world difference between the 2 shells, and I doubt the 24" G would be noticeably more dramatic in it's game killing the a 6.5G shot from a 20" barrel.
Where we will see the bigger difference in killing power on game from the 6.5 or the 6.8 and let's say a 270 Winchester or a 30-06, is going to be against larger game, not longer ranges on deer.
I have broken both front shoulder bones and dropped elk several times with 308s 30-06s 270s, but I seriously doubt either the 6.5G or the 6.8 SPC would do that much damage on an elk. They would both kill the elk, so I will not say it's not able, but will not be as dramatic. The 125 grain 6.5MM Nosler partition and several 6.8 bullets from 110 to 120 grains I have used, would be "effective" I am sure, but I would not want to shoot the close shoulder bone with either one on a large bull. From experience i can assure you an elk can go a VERY long way with only one lung.
I would choose a larger gun. Not that you could not kill elk with a 6.5G, but for myself, why would I want to?
I have a 6.5X54, a 25-06, a few 270s, a few 308s, a few 30-06s, a 300m mag, an 8X57, a 9.3X57, a 9.3X62, a 375H&H and a 404 Jeffery.
So speaking only for myself, I see no reason I would take the 6.8 or the 6.5G elk hunting. But I would not say to anyone else they would not work. If you are not unethical in shooting farther then you can place a perfect shot, I am 100% sure the 2 shells would do fine.