Yes, there are a LOT of options. And, there are even more options when you start including the AR10 platform. (.308 Win, 6.5 Creed, etc) So, which do you want and why?
First, let's tackle the idea of what we should be looking for out of a cartridge. I have my own uses for a rifle and they may differ from yours, which might lead you to look at the decision differently. For instance, you might need a rifle to kill multiple hogs that wander onto your property. You might need a rifle to kill hogs for food, ie there is meat left on them to eat. You might also need to kill small varmints, rather than hogs, primarily. You might need a gun for competition shooting. You might want a rifle specifically for CQB in your home, with no need to shoot more than 25 feet. Or, you could be like me and want a gun for self defense and the occasional varmint that is capable within 300 yards - capable, especially, within the short distances found inside your home. Basically, you need to decide how important accuracy, lethality, recoil, cost, and effective range are to you. You'll need to prioritize those factors based on the task at hand and the intended purpose of the rifle.
Now, to look at those intended purposes...
1. Hunters - If you're looking to hunt with your rifle, and you're looking at an AR platform rather than a bolt-action, you could be looking at medium to large game - anything from Whitetail Deer to Grizzly Bears. If you're that rancher or farmer that has a hog problem, you might fall into this category too. Basically, you need to drop the animal with 1 shot (Or, as few as possible.) If you start looking at what is an ethical distance to hunt at, given that requirement, we're not talking about 500+ yards for most hunters. So, realistically, any heavier round would do the job. So, supersonic 300 Blackout, 6.8 SPC, or 6.5 Grendel. (And, definitely AR10s in .308 or 6.5 Creedmoor.)
2. Varmints - If you're specifically trying to defeat varmints, any of the rifle calibers will do - it may take more than one shot of .223 for a larger animal, but it'll do the job just fine. In fact, well-placed .223/5.56 will take a deer as well, but it's not preferred for serious hunters. The fact is, they're varmints and you're shooting them because they're costing you money already, so why spend more on expensive target ammo? 5.56 or .223 will do here. I'd favor 5.56 for cost, the options available for 5.56 in the AR platform, and the ability to shoot both .223 and 5.56.
3. Survivalists - From a survivalist perspective, 5.56 is a great option because it's cheap, available, and can kill most animals you'll encounter in North America. It is a great all-around option for any purpose you can think of for a rifle. (Aside from sniping at 2,000 yards. Of course, you'd have to consider how many people actually CAN do that with any caliber.) I'd also go with 5.56 for the cost and to have the ability to shoot .223 as needed. Not to mention, being able to buy CHF barrels with the M249 chrome call-outs is so beneficial - long term durability!
4. Home Defense - I would go 5.56 here. It's cheap, readily available, and doesn't over-penetrate. You're shooting at short distances, in theory, so the need for a long-range scope and Sierra Match King ammo isn't really there. 300 Blackout is another popular option here and I have no issue with someone trying to save their hearing by shooting it suppressed and sub-sonic. 300 BO is a somewhat limited option because it basically has the trajectory of a thrown rock and there are much better choices for use at 200+ yards. However, specifically for home defense, it's a great option. Also, many people try to make a SMG (Sub-Machine Gun) out of an AR and chamber it in 9mm. Of course, people successfully defend themselves and their families with 9mm every year. That said, my feeling is that, if you are using a rifle, you should take advantage of rifle rounds and their lethality. Compare the muzzle energy of a 5.56 load (1200ish ft-lbs) and a 9mm +p+ load (500ish ft-lbs). The rifle cartridge is just so much more lethal.
5. Competition - .223 Wylde or .223. The stainless steel bull-barrels chambered in .223 Wylde are making serious headway into the competition scene. In many cases, it seems they are more accurate than simple .223 barrels and they allow for someone to fire most 5.56 ammo out of it. The key thing here is the accuracy, however. This chamber is providing excellent stability to the round due to the design of the throat of the barrel and the throat angle appears to be improving the life-span of the barrel with .223 ammo being used in it. That means less barrel changes - which is a great thing for a number of reasons, not the least of which is cost. But, realistically, for low-recoil, fast follow-ups, medium distance shooting, and extreme precision, one of these .223 chambers are the best choice. For 600 yards or more, it's a little different story. 6.5 Creedmoor is my pick beyond that yard mark. The Ballistic Coefficient and the extra powder are huge in aiding accuracy and achieving those distances. If you're shooting beyond a 6.5 Creed's effective range in a competition, you probably won't be using an AR for it.
6. Sniping or Hunting Dangerous Game - This is kind of like competition shooting and kind of like hunting, but with added requirements. Let me first explain for those that are wondering what I mean by sniping. Numerous situations can arise where one might need to snipe as a real option - ie kill another human being from a long distance away. The situations that call for a civilian to do this vary from pure fantasy to very real, though the situations are rare and I hope none of them ever come to pass for any of us. Some examples:
- Those that are familiar with the UT Austin tower shooting know that civilians with hunting rifles were asked by police to fire at the sniper. This allowed the police to storm the tower and get to the sniper, but any one of the civilians could have killed the sniper themselves if they were able to make the shot. This is one real life example of people needing to be able to return fire from another person with a long-range rifle. You might not have the clarity of a go-ahead from the police, but you might still need to be able to defend yourself against a sniper and defense of one's life is an inalienable right.
- In the event of a war, be it civil or an invasion, a member of the militia or any resistance group would be well-served to be able to take distance shots. A militia would need a sniper for the same reason our military needs them now.
- The infamous zombie apocalypse! Best to shoot them long before they have the chance to bite you! And, shoot fast because there's always a horde of them for some reason...
Overall, for most people and the widest variety of uses, I recommend a tried and true AR15 in 5.56. The durability of the barrels, the availability of parts, and the cost/availability of the ammo are all supremely important. If you are looking for a rifle to fill a special purpose, like distance shooting or hunting, then you have some other options that would do the job a little better. For subsonic ammo, you have your option as well. For me, there's always the siren's call of the bigger calibers, but I think 5.56 is exactly what I need. I want to be able to defend my myself against any animal (2-legged and 4-legged ones) that I would typically find in North America, be able to do so within 300 yards, and, especially, defend myself within my home. Other cartridges seem great, but the 5.56 is reasonably priced, effective, lightweight, good for high capacity, a low risk for collateral damage because it won't over-penetrate walls, abundant, and the benefactor of tons of AR accessories. (Magazines, barrels, etc.) Ultimately, you'll choose what's best for you, but I recommend you have several AR15s in 5.56 before you make the leap to something like .338 Lapua. And, unless you don't care about your walls or shooting through a wall and killing your neighbor's kid, 5.56 is better for home defense. Whichever you pick, pick the one that best fits your needs and train with it so you can use it effectively and safely.