My take on it is that the LC brass has visible heat annealing and has crimped primers but otherwise they are probably identical, given the velocity specs. The action on your bolt gun is going to be a good bit stronger than your AR, so I don't see a problem. [EDIT: See second post below.]
I'd do this first: Run both loads through your AR and chrono them at 10 feet to see if they are clocking identically and consistent with the labeling. I don't know what test barrel Federal used, so they are likely to run a bit lower than published, but I'd look for consistency between the two. Borrow a chronograph if you don't have one. Consider buying one. They are cheap now.
At least shoot both on a target and see if they shoot to the same point of impact. If so, and there is no discernible difference in recoil or how quickly the action cycles, then they are probably equivalent. Common sense.
Next: If all is well, then test fire one of the LC loads in your bolt gun and check for any pressure signs, such as flattened case head, shiny marks on the head, change in effort to lift the bolt, etc. The rifle will handle it, but if you get extraction problems or pressure signs, you will not want to consider the ammo interchangeable and should relegate the LC to your AR only.
Chamber dimensions are slightly different, but the ammo is the same dimensionally. The 5.56 ammo can exceed SAMMI pressure, but I'll bet that it does not because Federal knows it will be fired in non-5.56 chambers.
Caveat: I don't have a .223 bolt gun, so I've not tried this personally. Maybe someone here has direct experience in running 5.56 ammo in a civilian Model 70.