I have both. Never had a deer complain. I have quite a few rifles in a range of cartridge formats and I'd say these middle weight options are two excellent choices for pretty much anything. If I could keep only one, it would be .... drum roll please.....
The 7mm. Why? Easy: I like that rifle more. One is a T3 light and the other is a Finnlite with a particularly nice Zeiss on top. Yes it's that stupid. Both share the same moderator. I home load and just found that actual velocities for me in the .308 were a bit low against the books. I switched to a 130gr bullet and it's a cracking set up. I've no desire to try and push out a 200gr RN from a .308 - I have a .300 Win for that. The 7mm takes a 140gr bullet and give me just that little bit more confidence in practice on longer shots. The tables say otherwise. Frankly, I'd perhaps swap your 168s for some 150s. Gain a bit of velocity, lose some recoil maybe and frankly not sacrifice anything.
Would I sell a .308 to buy a 7mm-08 no. Would I sell a .308 Tikka to buy a .308 Sako, ahh well, that's all about want not need isn't it.
Short version is - sometimes shooting is about what's going on in your head. If you think that 7mm-8 will be better then it will be. Doubt is something that I try to eliminate where ever I can. Does tea taste better in a china cup than a chipped mug? Of course not, the question is, do YOU think it does.
Sorry for this being a bit odd, I'm in a rather reflective mood today. There's an interesting difference between a choice and a decision. I'll share it with you, I can see you're all keen.
A choice is where the outcome doesn't actually matter. Presented with say two options, the outcome of which will do the same thing, you can literally flip a coin for it. "Ooooh I'm hungry, so many thing on the menu. I can't decide whether to have the fish or the chicken; I love them both" That is not a decision. It's a choice. Pick one
A decision is where the outcome matters due to its implications. So in this example Mike, I'd say it's really just a case of choosing.