The 308 is a great round for any deer in NA. I would stick with the 150 or 165 grain bullets for deer. Anything less is most likely be a varmit round and not a good idea to use on deer.
The 110-grain bullets in 30-caliber are thin-jacketed, intended as varmint bullets. Odds are they'd fragment on bone on the way into a deer. Not a good choice.
No kidding. I thought I had some 110s that I used in comparison to the 125s on varmints a few years ago. I can't even find a factory load in 110 now, so I may be misremembering. There was no noticeable difference in damage/performance. Now I'm wondering if I still have the box, I'll have to check. If they are actually fragmenting bullets then I'd go with the next step up.