Now that we no longer need to use a 100gn bullet in Scotland all the challenges with non-toxic and 243 Win are now in the past.
There are plenty of good 80 to 90gn non toxic bullets that will perform very well in the 243. I have used the Peregrine 100gn VRG3 in my 243 on one Sika Stag. It punched straight through heart lungs and shoulders and it ran a few yards and collapsed dead. The VRG3 is a flat nosed bullet so BCs not optimal for longer range if that matters. It doesn’t for me - 200 is plenty far enough.
Having seen how Peregrine and Fox bullets perform in 223 at 50 gns and 7mm at 130gn, I have no doubt that an 80 ish grain 243 bullet leaving the muzzle at about 3,000 fps will punch through any British deer causing sufficient damage to effect a quick kill.
Would a bigger bullet be better - perhaps. But given good shot placement there has never been a lot of difference between a 243 and 308.
But with monolithics the challenge’s of bullet blow up and lack of penetration of the 243 are much reduced.
Or put it another way, the difference between a 12mm, 14mm or 16mm permanent wound channel through heart, lungs and major blood vessels (assuming bullets opens to 2x diameter) is not really going to have a significant difference on life expectancy of a deer.
And either side of the permanent wound channel will be the temporary cavity - again a slightly bigger or smaller is not going to make much difference.
If you have a good 243 that you like shooting then just keep shooting it. 308 can have enough recoil that some may struggle to shoot it as well as the 243.