Several things would be different.
First, the case capacity would be different - so using a full-case of something (to eliminate the varialbe of powder position) would use a different powder - for better or worse.
Second, the shoulder would be different - generally the sharp shouldered cases don't stretch as much as would something like the 30-06.
Third, the case walls would be a little heavier with the 308-LN.
Fourth, in this case the neck/throat dimensions were custom matched - good if one plans it right vs. what you get from off-the-shelf.