Wheatgerm,
I believe Varget would be fine in both cases. But as Kevin said, it may not be absolutely optimum in both cases with every bullet weight.......but it certainly will work in both the 223 and the 243, also works very well in the 22-250 class of cases. If I had to pick just one Hodgden powder for everything from 204 to 223 to 22-250 to 22-250AI to 6X47AI to 243AI to 6mm AI..........I think thats all of them.....?....It would be Varget.
I've had great luck with the 243 and AI version with 4831 SC with the 105 bullets.
4350 is very good in that case size, but harder to meter with a powder measure.
FWIW, R17 is right in that category, between the 4350's and 4831's.
Even though Varget should work, you might not get the velocity you would with the slower powders and the heavier 105-115 bullets.
I guess if it were me, and I had alot of R17 already, I'd try it in the 243 and buy a faster burning powder just for the 223. But I am way more likely to shoot a bunch of 223 than a bunch of 243.