If you have one calibre with a Bartelin (because it seems the most favoured judging by the responses?)....and the other rifle tubed with a Border (or any make of barrel for that matter) I would be very interested to see what 'you' determine as which is the best barrel....and then see what someone else who fires them determines as which is 'the best'
Most new barrels in the calibres you mention will shoot .5" with careful load development in the right hands shooting in ideal conditions...and that includes factory barrels...However, put your new, 'best re-barrelled' rifle in the hands of a shooter who struggles with point of aim, for whatever reason, and it's then you'll discover you've been advised of well-meant but, personal preferences.
As for re-barrelling your .'bog-standard' 243, why? ...It's approx the same cost to buy a new Tikka as it would be to re-barrel. A new Sako produced barrel will print as accurate a group as any custom barrel, all specs being equal. Economically speaking, better off to buy a new rifle