To answer your question both are .532" bolt face.
Both cartridges need to be in a medium length action at least or long action preferably.
The only thing that makes the 6.8 western even remotely viable or "cool" for anything other than hunting is 3 bullets. One from Berger that's rarely in stock and weights 170gr. And one from Sierra thats 175gr. And a 150gr offering from badlands bullets that's probably the most interesting of the 3. Also fast twist .277cal barrels are not very plentiful. 6.8 western is essentially a 270wsm with a faster twist barrel in Saami dress.
Go with a 7prc or 7 sherman short or 7 sherman max or 7 sherman mega or 7wsm or 7saum or 7rum or 7stw or 28nosler or 284win or 280ai or 7-08 or 7saw or etc.........long before you mess with a 6.8 western just for punching plates at distance! 7mm has 30x the bullet selection and barrel selection. A 180gr 284cal berger at 2875fps has won a crap ton of 1000yd matches for a reason. Also the 190-195gr bullets in 7mm have a BC that rivals things in 338lapua class bullet territory.
What cartridge was your rem700 action originally chambered for?