I don't own any falling block rifles in un-rimmed chamberings other than a Ruger No.1 in 458 Lott.
The Ruger works very well with rimless cartridges and I think I have seen Hagn actions in rimless chamberings as well so it really comes down to personal preference but the traditional choice would be the rimmed cartridge.
If you are fixed on the 7mm but want some extra power over the 7X57 you may consider the 7X65R.