I agree with what Sam says with regard to twist and bullet weight. In your case you have a .222 Rem converted to a .223. The .223 has a larger case and will give higher velocity. So with respect to stabilizing a larger bullet the converted rifle will be better than the old .222. It would seem a bit strange that Remington would have put a 1 in 14 twist in the gun, and you may want to do a bit more research to see if that is really what it is. You could also try marking a cleaning rod and to check how many inches it takes to get one revolution.
The velocity effect on spin is not really all that much. Berger for example rate the spin required based on the bullet weight and design and don't give a velocity required. Check this link out. It says 50 and 55 are ok with 1 in 14. Berger Bullets
If you want to figure it out and have access to Excel here is a formula developed by a Don Miller to determine what twist you need for the various bullets and velocities. I think it is a bit conservative however, and I have been unable to match the twists recommended by Berger.
Sg - is the stability coeficient and should not be less than 1.4, but more is ok
C4 - Caliber in inches (.223 for both .222 and .223)
C5 - Bullet Weight in grains
C6 - Bullet Length in inches
C7 - Barrel Twist in inches per turn
C8 - Muzzle Velocity in fps
C9 - Temperature in degrees F (59F normally used)
C10 - Pressure in inches of mercury (29.92 normally used)
For interest I ran a 55 grain through the formula assuming 0.7" length and a .222 velocity of 3100 fps. It came out at Sg equal to 1.15, or not enough. However when I increased velocity to 3300 or .223 speed, it only increased to 1.17 or an insignificant difference. And at either speed it needs about a 1 in 12.5" twist to reach the 1.4 for Sg.
So I think your short answer is that the barrel was made slightly better if anything by rechambering. A 1 in 14 twist if that is what it is, should give you the best possible accuracy in the 50 grain bullet weights, better than the faster twist barrels. However it will be limited to 55 grains or so. You will want to stick to the flat base, shorter bullets.
Here is a good link where they discuss the twist rates required for a .223. 223 Rem + 223 AI Cartridge Guide