I have had a 243 since the mid 1990’s and a 223 for about 4 years. 223 is a lot quieter.
Terminal effect on Roe deer is pretty much the same. And would suggest that choice of bullet has far more effect on end carcass damage. I cannot see any terminal difference on Roe between a 51gn 223, and a 75gn 243 Peregrine VLR4 bullet. Perhaps if I took out a micrometer and very accurate scales I could tell the difference. Ditto on crows. I have yet to shoot a fox or a muntjac with these bullets, but suspect similar result.
I must admit to really liking the 223. Its easy to shoot, cheap to run and deadly. If it wasn’t for the legalities, I wouldn’t hesitate to use it on bigger deer at closer ranges (100 or so metres).
The 243 however is a big step up in power, noise, recoil etc. It is at the bottom end of 308 series of cartridges and with 75gn to 100gn bullets will and has pretty much been used all over the world.
South of the border you can use the the optimum 80 to 90gn bullets whether lead or copper on any deer and it just plain works. In Scotland we are slightly hampered by the 100gn min, which for lead free means Peregrine VRG3 bullet, which is not really an issue unless you are into long range sniping on big deer, and 243 is not the job.
If you are just shooting vermin and small deer (muntjac and CWD south of border, Roe in the north) then go with 223.
If you want one rifle for everything 243 or to be honest these days, the 6.5cm or 308 may be a better option.