To give you a comparison of what I found when upgrading from the stock .223 Savage 1:9 varmint barrel to the Shilen 1:7 select match barrel. Stock barrel on top.
Obviously the quality of the barrel will have an impact on accuracy potential but the biggest benefit to me was the ability to shoot the longer bullets with the appropriate chamber dimensions and twist rate.
A note on sticking with .223
After I had been shooting F Class matches for a while my son and daughter expressed an interest in trying it. I had already made high master shooting a custom .308 so I offered that to my daughter and set my son up with the aforementioned .223 Savage. I had just gotten my 6BRA so the timing worked out great.
As they improved (and both also made high master) I offered to have a custom rifle built to whatever caliber they wanted. They each chose to stick with the rifles they had in .308 and .223 respectively for very similar reasons.
My daughter got satisfaction shooting the heavier recoiling .308, occasionally beating the crusty seasoned F/TR competition, and the attention that accrued to her for doing so.
Likewise, my son also appreciated shooting his .223 Savage against all of these purpose build custom .308s, being competitive and winning a few matches.
So, I get where you’re coming from.