I have both. Shot a few caribou with the Wby, it works well as I'm sure the 25/06 would as well
If money is no object I'd get the Wby.
Up here a box of 257 Wby runs ~ $75 compared to $28 for 25/06.
With the ability to make Wby brass from 264/7 Mag brass the argument fails about high brass cost.
I've got a 99 TD in 250.
The only 100 grain bullet I've had group decently is the bulk Rem CoreLocts. 1.5" at 100m with an old Redfield 4x.
85 Noslers and 75 V-Max's shoot good as well but IMO I think they're too lightly constructed for deer.