My "heavy artillery" for pigs,goats,deer,feral horses and donkeys plus feral cats is either my 30/06AI or my CMC Mountaineer in .270 as these 2 calibres are probably along with the .308, 30/30 and .243 are probably the most commonly used calibres here in Australia for game in the above mentioned calibres.
I've also taken pigs with my .222 but that was all I had in my hands at the time same as when I dropped a couple of piglets and a sow with my .22 wouldn't really recommend it but....................
I used to own a commercial BSA/Parker Hale .303 on a Mk.4 No,1 action which served me well on pigs and goats but I sold it to help pay for my 30/06AI wish I never did as it was a real good pig buster with 150gn hand loads and the 10 shot mag but I made up and bought and refurbished a Mk3 No.1 SMLE and 180gn Pro Hunter projectiles but am yet to christen it on pigs or goats.
With Australia's multitude of game from rabbits up to Asiatic Water Buffalo no 1 calibre is "best" because buffalo can absorb a lot of lead especially .458's and can generally soak up 3-4 shots before they drop and we're talking a beast that can weigh up to ton in weight and has the ability to ream you a new orifice when pissed off.
Here's just a list of what we can shoot here in Australia ranging from thin skinned up to almost "bullet" proof and the reason why no 1 calibre will do it all here.
Rabbits.....22 cal from rimfire up to any high velocity wildcat/varmint round plus shotguns.
Feral cats........... as above.
Hares........ as above.
Foxes.... as above.
Kangaroos and Wallaby's.................222,.223 and bigger .22 cals but for use must be head shot.
These are protected here but can be culled under special permits for species culling and pet/human consumption and are thin skinned.
Don't believe anything the animal humper/lovers say that they're scarce because they aren't and can breed like fly's when conditions are right.
Goats............probably a .222/.223,22/250 with heavy pills,.243 upwards but like any thing this size hit in the wrong place and they'll carry lead for a long way.
Pigs........... as for goats but better with bigger .24 cals upwards because of the fact that some pigs have very big pads on the shoulders and a pig covered in mud is like having extra armour so a good SP or HP in a heavy weight would be a better proposition.
Deer..........minimum calibre for legally hunting deer in Australia is .243 but they have been taken with .222 and .223 but these are way undergunned in my opinion.
We have a fair range of deer here ranging from Hog Deer(roughly the size of a Labrador), Fallow,Chital,Red and Sambar and for the likes of Red and Sambar something around .308/.270/30/06 upwards is preferred because these CAN carry lead from a bad shot and can also from a lethal shot still run for a fair distance on pure andrenalin in thick scrub where they favour.
Camels and Donkeys.............. probably 25/06, .270 upwards would be a good starting point.
Water Buffalo,Banteng and Scrub bulls.......... This is where you start thinking Africa type calibres as in the big .30's(.338 as a minimum with the biggest pill available) as a bare minimum but probably .375 with a 300gn pill as a better starter.
So as you can see we have a bigger problem with "what is best" over here with probably 3-4 calibres being more like it but more is better.
The other thing that fascinates me with you Yanks is your fascination with the .223 round as a seemingly "go to for everything" round.
In Australia we treat it as a varmint round good for busting rabbits up to small pigs and like the 22/250 that overtook the .220 Swift it seems that people are just following trends as the .222 has been overtaken by the .223 even though there's not all that much difference in performances.
The .223 seems to handle the heavier 55gn + projectiles better over the .222 but that seems to be it.