Typically, when competing in Score, 30BR bullets are 112 to 118 grains with 34 to 35 grains of H-4198. Relays are 7 minutes long. Many shooters finish their 5-shot record target [including sighters below] in a minute or two and some in only seconds while conditions hold. Thomas "Speedy" Gonzalez didn't get his nickname by sitting around waiting for barrels to cool or compete only in cool windy weather. Texas can get extremely hot during the competitive season. [outdoorsman]
Fair enough as they say. Let's run the figures. Using a 118gn Berger over 35gn H4198, QuickLOAD predicts 62,000 psi which doesn't seem unreasonable from my own experience of other BR cartridges. Run this combination through mikecr's barrel life calculator (obtainable if you do a search in the Bulletin elsewhere on this site) and assume a shot every 10 seconds (faster the rate of fire, the lower the life)
Estimate - 5,085 rounds. Pretty well as per what you said.
Run the OP's 308 155gn load through QuiockLOAD and we get a PMax calculation of 58,300 psi - in line too with my own experience and why most FTR shooters use a faster burner than VarGet, (H4895 or IMR-8208 XBR the favourites) to get another 150-200 fps than the TR / Fullbore sling shooters run their smokepoles at, and sticking this lot into the barrel life calculator, we get
a shot every .......
10 secs: 1,188 rounds
20 secs: 2,376 rounds
30 secs: 2,626 rounds
The calculator is a simple model and takes no account of bullet weight. All other things being equal a heavier bullet wears barrels out faster than a light one. But, on the other hand, the slowest rate of fire the model allows is 30 seconds. In the GB two or three on a mound system, extend that to 90 seconds or more which increases barrel life further.
So, to compare .30BR with 118/H4198 to 308 Win with 155/Varget is a total apples and pears job. Varget is a considerably hotter burning powder (4,050 KJ/KG) compared to H4198 (3,860) and the powder charge weight in 308 is 31% higher, but the increase in energy input is of a greater magnitude still. As both cartridges are 30cal, the comparison is valid as the energy is funnelled into the same bore area.
However, as noted, in real life the ultra light (by 308 Win standard) bullet will increase the BR's life even more in practice, and generally short-range BR rifles have short, but fat and heavy barrels - a nice large heat sink. The sling shooter's 308 model normally uses a light or standard Palma profile - longer so total heat abosption may be the same, but likely to get hotter faster in the key are around the throat and chamber as there is a lot less metal around the areas that heat most and whose continued good health are the critical life factor in a well made match barrel.
The calculator figure for 308 with Varget also puts the GB shooter's claim of 10,000 round barrel life in the rifle he used 'there' (the SWN I assume?) While I wouldn't disbelieve him on the basis of what some GB TR shooters squeeze out of their barrels (44gn cool burning Viht N140 and a 155 will see a barrel last a LONG time especially in the UK environment), but I have measured bullet jump to the lands on many genuine high round count GB shooters' barrels and seen some sectioned by gunsmiths / barrelmakers. And believe me, we're not talking thou's or tens of thous freebore in this sort of scenario - it can be an inch plus, and I've seen three inches with no rifling left at all! Amazingly some of these rifles still shoot and hit the black at reassonable distances, but on reflection, I find it very difficult to believe anybody with a true 10,000 round-count barrel being so stupid as to (a) enter one of the world's largest and most prestigiopus L-R match fixtures with its entry of international team level shooters, and (b) fly 6,000 (?) miles to compete in this match with such a barrel!