Well I was going to say 243 but you already have one. In the grand scheme of things it makes little sense to go from a 6mm-08 aka 243 to a 7mm-08. So outside of the terrible twist rate that factory 243 Win has been cursed with forever. Clearly if you are building from scratch you can have any twist you want to future proof anything that said I do not think 7-08 and 308 Win have ever suffered from that.
6mm, 7mm and 7.62mm???? You see were I am going? The 25-06 is like wise a light recoiling machine but has also suffered from stupid slow twist rate and until recently shortage of heavier bullets.
Given your choices ballistics are slightly better for 7-08 and recoil is slightly lighter but you give up the option of loading heavy bullets. I understand the 308 Win is not the 30-06 or a 300 Win Mag so it does have it limits on the heavies but there are times where they do make a LOT of sense.
Is this for a boy or a girl?
What is their build my oldest son is 6 foot 2 220lbs. and very fit and he was always a big boy just like me. My twins are 5 foot 6 and 135lbs at the age 19 and they were never large for their size they take after their mothers side. I would never build the same rife for those two different builds. For instance when my oldest son was 11 years old I let him shoot my 45-70 and it was not an issue for him at all it might as well have been a 243 Win. For my twins when they were maybe 14 I got them a Ruger American in 243 Win and hoped they could handle it. Their short limbs and super light weight being the issues.
Is this going to be a short 16-18 inch brush gun, tractor gun, truck gun, scout gun or are we talking 22-26 inch open country sort of situation.
Even though I really like the 7-08 in almost every way I own 2 308 Win rifles and both of them are heavy barreled one is F-TR rifles clearly no choice the other is an ancient Silhouette rifle. My Sons 308 Win was an attempt to check off his police, Army, Marine Corp "Tact-i-cool" boxes as a very young man and yes it is a Remington 700 the only Remington I have purchased in my 48 years on this Earth. Truth be told since you can load the 308 Win with everything from 110 varmint bullets to 208gr ELD/VLD's to 220gr. round nose ammo it clearly has advantages to 7-08 in flexibility.
Do you shoot F-Class? Would you maybe like to in the future with a young boy or girl? F-TR might be something to plan on?
So if no to F-TR all of that above said I would still probably lean towards 308 Win as boring as that sounds for sheer flexibility. If you reload you have almost unlimited choices for components and if you do not you again normally non-SARS-CoV-2 related situations you can normally find everything from mild to wild in factory loaded ammo and match grade ammo in 308 Win. Even given the last 500+ days I can find 308Win and 5.56/223 ammo easier than any other chamberings I have not seen any 7-08 ammo on the shelves in the last 500+ days in my area it was only 2 weeks ago that slugs rifled slugs reappeared locally no sabot slugs mind you and buck shot has not reared it's head yet. For the last 500 days it has been mostly birdshot, 350 Legend, 45-70 and 308 Win and even then no selection in brands or weight and only every other month. In fact I just got 3 325 count packages of 22LR ammo the other day first time in 500+ days that 22LR has been available to me locally.
So a lot to consider that you prob. would never have thought about 500+ days ago!