I'm a big AR fan, and I think the Sig is slightly better.
Now, assuming all things are equal (build quality) ..the Sig is a better design.
A major weakness of the AR is the bolt design. The lugs and cam pin hole are a weakness. You can counter that claim by suggesting that you should just follow the maintenance schedule and understand a bolt is only good for 5,000rds or whatever. The other weakness is the gas system which is filthy. The filth isn't really the problem, but the fact that it blasts away the lubricant and heats up the parts. The counter to this is, that a properly lubricated AR will run totally reliable for double the expected load-out (480rds). Which it does and should. The bolt becomes extremely hot, which effects the lifespan. But more importantly, ever shot is blasting away lubricant and adding gritty carbon. The operation becomes significantly less and less slick.
The Sig takes a lot from the AK. That is evident in the bolt design. It is very solid. I can't imagine breaking an AK or Sig bolt. The extractor is also much stronger.
One weakness of the Sig or most piston systems is that the recoil spring is subject to heating which alters its characteristics. Weakens it sooner, changes its tension. The other weakness is the piston itself. That is an advantage of the gas impingement system of the AR. The AR has a single gas tube. That's it! No piston, no op-rod, no spring, no knobs or screws. Less to rust. Less to break. And a lot LIGHTER. Piston systems weigh more. Another weakness of piston systems is that they are more ammo sensitive. This claim is made of the gas-impingement system but I just don't see it. It is an issue with piston systems. The Sig can be adjusted when the action is slowing down. Increasing the gas flow to blast out the crud or to function with weak ammo. The AK system doesn't care.
Overall, the AK system is the best. The piston is easily 2x over-built and will not break or bend. The recoil spring is kept away from the gas system, so it does not heat up and fatigue. It has a robust bolt that will not crack or shatter. Has a strong extractor. And a fixed external (from the bolt) ejector that will not clog up or break. Add in tapered cases, and feeding and extracting are now even easier...but that is not part of the rifle's design but rather total platform.
HA! Sig vs. AR and the AK wins!!!
Unfortunately, the AK is no where nearly as easy to modify and make as ergonomic as the AR, and even falls well behind the Sig.
The Sig 556 has had some issues. Still a young rifle and they pretty much have the bugs worked out. Not so much design flaws, but rather QC and build quality/parts quality. I do not care for the handguards at all. A lot of people are paying $100 to get original Sig 550 handguards. Making the stock compatible with the AR-15 is a smart move. They should have taken it a step further and made the grip compatible also -- while keeping the Sig trigger which is a better trigger in both pull and feel.
Sig claims the barrel finish is superior to chrome lining. I'm skeptical about that. Usually whenever a company doesn't chrome a chamber and bore they make extravagant claims about whatever alternative process they use.
The AK is an anomaly in that compared to pretty much every other weapon system past and present, it is built to survive with the least amount of armorer support. The AR-15 system has the U.S. Military behind it, which is the greatest logistics master since the Romans. Most other weapon systems are what they are and function as a State's military combat rifle. It will be used by professional or well-trained soldiers within the military sphere. That is perhaps why the AK was and is so successful among rebels, militia, guerrillas all over the world in remote areas. It works without the support. It was designed with conscripts in mind from the Soviet WW2 experience.
The AR would have been a lot better if the lugs were reduced in number and then increased in size as well as the bolt being beefed up, particularly in the cam pin hole area to eliminate or double the service life of the bolt from cracks. The other area is the extractor. A stronger design would have been better.
Aside from rebel warfare in remote areas, or mass conscription of peasants ...the Sig and AR will serve the American civilian just fine on the range or for home defense or during a disaster situation. If Western civilization melts down, you have more to worry about than where you will get your spare parts for your AR-15. If you can't get spare parts for you AR-15, you cannot get ammo either and if you can't get either of those, chances are you can't get food either. Sort of goes hand in hand. But I digress.....
The point is, where one really shines as better than the other is in situations that aren't likely or you're likely to have to cope with.