There are several factors in deciding what rifle to go for for a foxing gun. I'll try to outline those that apply to the choice between a .243 and .223 calibre rifle, given that the land is safe for both. There are other similar calibres and choices (Ackley improved etc) but for the purposes of this review, I'll stick to these two as the debate often compares these two different 'types' of calibre.
These factors are cost, availability of ammunition, ease for reloading, trajectory and windage, noise and recoil, effect, accuracy and versatility:Costs and availability of both rifle and ammunition
In my opinion; the cost difference is irrelevant. Most shooters won't be shooting more than a hundred foxes a year and given a .223 factory load might be 10 - 20 pence cheaper than a .243 load, that will mean they have saved £20 in total. Even if they choose to reload, the difference is not significant. Costs do come into consideration when they are used more often than this, ie; for vermin shooting but this isn't under discussion here. We're talking about a foxing gun.
In terms of choice of rifle, in the UK at least, both calibres are very popular so cost for both should be similar, either new or second hand.
Ammunition availability is the same for both calibre with perhaps a slightly larger 'off the shelf' selection for the .243 but nothing really significant. Both calibres are easy to reload.Trajectory and windage.
I have a .243 for foxing with NV because it gives a very very flat trajectory with 58 grain bullets. Using NV makes life difficult in terms of range estimation and a 'point and shoot' calibre is very useful. This applies equally when lamping. The 58 grain VMax is flat out to 250 yards and not bad out to 300. Stoke it up with an 80 grain bullet and you could comfortably shoot out to 500 but that clearly isn't what you're looking for. Needles to say, the flat trajectory of the .243 is the biggest advantage over the .223. Without the need to estimate range, you simply point and shoot.
Flat trajectory aside there is also the problem of wind. The longer, heavier bullets in the .243, even the 58 grain bullets will fly better than most .223 bullets. Yes you can load 70 + grain load in .223 (with the right twist rate) and they are extremely accurate but bugger all use for fox shooting as they're loopy as hell. I can get a .223 cal 36 grain Varmint Grenade at 4040 fps to fly as flat as the 58 Grain VMax in .243 but with even a little wind, it's poor beyond 100 yards. The ideal bullet in .243 for fox shooting is the 62 Grain Varmint Grenade (powdered Tin Copper composite) or a heavier standard lead bullet where there is a nice flat trajectory with very little wind deflection.Noise and recoil
Noise is similar in both rifles and both can be effectively moderated, Recoil is heavier on the .243 but on a foxing gun, you can afford it to be heavy as you won't be stalking with it. The heavier it is, the less you have to worry about recoil.
Some folks say that the .223 will allow you to see the bullet strike better and I believe this is true of the .223 in day time. When shooting at night in the lamp you rarely see the impact anyway, as the flash and smoke can temporarily blind you and it's also dark so harder to see clearly Effect
Type of bullet is also a consideration for foxing. like I said, I have 2 .243's. One I use for woodland stalking with 100 grain soft points. These are useful for longer ranges but given that they don't fragment, they can often pass through a fox and it wont fall over instantly. The .243 58 grain VMax carries enough weight to avoid too much wind deflection but because it explodes on impact, you get very very few runners. It also reduces the risk of ricochets as it tends to break up on impact with anything. These fragmenting bullets are effective in .223 as well but given that they are at their best driven fast, they come into their own in a .243.
Most normal people won't be eating fox after shooting them so the fragmenting bullets are preferable in terms of humane kill. A fox in bits is normally a dead fox; one with a hole in it may not die instantly and if it runs you have the moral obligation to recover and humanely dispatch it. Far fewer foxes will run if shot by a fragmenting bullet travelling at high velocity.Accuracy
The accuracy argument doesn't hold as this is bullet, load and rifle specific. What works in one rifle may not in others. I believe that to get accuracy, you need to try a good few different loads in whatever gun you have until you find the right round to suit. This applies equally to .223 and .243 or any other calibre for that matter. My .243 foxing rifle is very much as accurate as my .223 and will generally perform much better at longer range than the .223 (again dependant on the twist rate of the .223 and weight of bullet).Versatility and usage
Outwith the UK, there is a debate regarding versatility as both rifles fill different purposes in terms of varmint control or serious hunting. the .223 in any guise or twist rate is a serious Varmint rifle. In many ways it is now old technology and has been well and truly trounced by the arrival of the new .20 cal rifles. It does however offer the vermin (varmint) shooter a useful medium range (300yard) varmint rifle with the added capability of taking small deer and larger predators (fox etc).
The .243 rifle, with its heavier bullet capability can floor any species of deer alongside it's extreme capability against predators such as fox using lighter bullets. It is questionable however that the user will shoot small vermin with this calibre. Once the numbers of rounds fired begin to mount the difference between these two calibre in terms of cost become significant, with the .243 running at approximately 30% more than the .223. It does however have a better range capability than the .223's (depending upon the twist rate of the .223). In my experience, there is little need other than bragging rights to be shooting vermin at ranges beyond 300 yards anyway and there is a strong moral argument against this.
For foxing in the UK, both are adequate and recognised by the Home Office as effective tools for the job. Given that many foxes are shot at night using a lamp in the UK, there is no question that the .243 is a better choice. It has the flattest trajectory of the two, giving the shooter a 'point and shoot' option for a longer range. Shooting beyond 300 yards at night requires a great deal of skill and several operators (driver / rangefinder, lamper and shooter) to allow for accurate identification of a fox so I am discounting shooting beyond this range.
The advantage within the UK of the .223 however is that in many areas, the Licensing Authority (police) may authorise the .223 for use as a vermin control rifle. this gives the .223 calibre an advantage where the shooter has no intention of shooting larger deer species. The .243 is rarely issued as a vermin control tool.
Check with your licensing authority if they will consider licensing the .223 for vermin. If they do and you have such a use for it, the .223 may be a better choice. If however you only intend to shoot fox, then consider the .243 as a better option (also 22/250, 220 swift, 25-06 or .204 Ruger to name abut a few other options with similar performance). If you also shoot deer regularly, there is no question whatsoever; the .243 wins every time.
Here are the actual trajectories for my rifles for the 58 Grain VMax in .243 and the 36 Grain Varmint Grenade in .223. They are very similar out to 250 yards, except the 58 grain .243 bullet will deflect much less in wind. Note: A 55 grain VMax in .223 cal will not give such a flat trajectory as the 36 grain bullet so is not worthy of comparison.
Varmint Grenade in .223:
58 Grain VMax in .243:
As an aside; here is the trajectory for my .243 with 100 grain Nosler partitions: