For 300 yd I would go with the 223,if you reload or factory you will come out ahead.I have a 10fp in 223 and it has a 1:9 twist.It shoots from 40 gr bullets to 75 gr bullets.So if you have the chance to shoot farter than 300 yds it will work.
I also have a savage 22/250 which has a 1:12 twist,so it wouldn't shoot the heavier bullets.I think now they have a couple models that they do offer different twists in.
Both have varmit barrels but the 10fp is much lighter to carry.
I gave a little over $400 for the 223 years ago and over $600 for the 22/250.