The 7x47 is very efficient. Really drives bullets fast considering its size. Don't let the smaller size turn you away. There is a very good article here about it and barrel lenths.
The rule of thumb on this matter is that all other things (peak pressures, barrel lengths, use of appropriate powder grades with equivalent specific energy ratings) is to take the percentage change in case capacity and divide it by four to get the percentage change in MV.
The 7mm-08 case has around 15% greater capacity than the 7X47L equivalent, so will produce 3.5-4% higher MVs; the 7mm-08AI offers a 20% increase, so will give 5% higher MVs.
As we're talking reformed small primer 308 'Palma' brass here for the sevens, the three versions can all be run at the same pressures. Using LRP Remington, Lapua, Winchester etc brass would see the two 7mm-08 versions loaded to 3-5,000 psi less than the 7X47 Lapua to get half decent case life.
So, if the 7mm-08AI gives around 2,800 fps with the 140gn Hybrid, Benjamin's objective, the standard non-improved version will give around 30-45 fps less at similar pressures in the same chamber and freebore; the 6.5X47L based version around 140 fps less all other things being equal.
I run the standard 7mm-08 in a 31-inch barrel F-Class rig. Can't say what the freebore is as it was manually 'throated' to see a 168gn Berger VLD optimally seated and just 'in' the lands. (COAL = 2.975"). As it turned out, the barrel doesn't like this bullet much, so I've ended up using the new 160gn Sierra TMK at 2,830 fps over nearly 50gn of Viht N160 in reformed 'Palma' brass, a relatively mild load and which should keep barrel life good. If my wind reading is on form, I give 6.5X47Ls, Creedmoors, and 7mm SAUMs and WSMs a good run for their money in 500/600 yard matches on a range well known for 'tricky' winds.
The only LRP brass I use now is for my 200/300 yard load of the 150gn Lapua Scenar L also at not much over 2,800 fps over Czech Lovex SO65, a relatively slow burning and bulky single-based powder. The Scenar is a very high drag model for its being a relatively recently introduced seven, but the combination shoots very small groups indeed and works well to 300 yards in F competition too.
Both loads produce little recoil in a 20lb+ F-Class rifle making them very easy to shoot. They also allow the use of modern wide bipods with no loss of control or stability over a front-rest, and reduce the kit weight that needs to be humped around in an uphill moorland range that doesn't have vehicle access to all distances' firing points.
Having played around with 175s/180s, I came to the conclusion that the standard case is just that bit too small capacity to hold the required amounts of slow-burning single-based powders. The AI version would be a boon if running this bullet weight. The other answer would be to go to Reload Swiss RS60 (Alliant Re17), but I've done my best to avoid the hotter burning / high-energy grades. If I need to shoot this bullet weight, I use a 284 rifle.
For informational reasons, I'll test three higher pressure / MV loads with the 160gn TMK over the next few weeks using the soon to be lost to us IMR-4831, plus European manufactured Viht N550, and Ramshot Hunter. It should be feasible to get to 2,900 fps plus with the small primer brass, but even if it does so and works well, I don't intend to use these loadings in this rifle. (2,900 fps with the 160 is the equivalent of 2,735 fps with a 180gn bullet using ME generated as a rough and ready calculator, so is still a fair bit short of Benjamin's AI performance target.)
I know from earlier tests that RS60 / Re17 works well with this bullet and the 175gn Sierra MK and gives respectable MVs, but again have no desire to trade a significant amount of barrel life for the MV gains when I have a 284 that does it at lower pressures and temperatures with Viht N160 (160gn bullet) or N165 (175/180s). I also noticed that with half-decent performance loads with 175/180s that subjective recoil increased noticeably over the 150/160gn bullet loads to the point where I started to feel that one of the little cartridge's key benefits was being sacrificed for the extra ballistics performance.
I came to the conclusion some time back that if only ballistics are counted, it is better to keep the smaller capacity cases in 6.5mm calibre given their ability to produce over 2,800 fps MV with very high BC 140gn bullets. The 7-08's inbuilt advantage is barrel life over them. To start to get external ballistics advantages from a move up from 6.5 to 7mm, the AI variant of the 7mm-08 is needed at the very least, or a move up to the next case size - 280 Rem / 284 Win