I own and like both platforms. In general, when talking about your typical 5.56/.223 AR vs the 7.62x39 AK, here are some advantages/disadvantages:
Initial cost - Talking about a basic, non-fancy rifle, you can pick up a Century WASR-10 AK, 2015 manufacture for about $600. I have one, and it is good quality. Some of the old WASR rifles that came into the US years ago were crap, but check the reviews for the new ones online. They are now decent quality rifles. Your basic AR can also be had for around $600, maybe a bit more. I have a S&W M&P15 Sport that I picked up a year ago for a little under $600. Works fine, I use decent quality brass cased ammo and haven't had a problem.
Ammo cost - AK ammo is cheaper. In bulk, 23 or 24 cents a round is a ballpark price. AR ammo is about 38 cents a round. You can get steel case AR ammo for about 28 cents a round, but some ARs will run it and some will not. More on that later.....
Ergonomics - This is subjective, but I like the feel of my AR better than my AK. The AR platform is a lot more modular, you can easily attach rails, foregrips, different stocks, etc to get it tailored just right. You can also do this to an AK, but there are not quite as many options due to the basic design of the rifle.
Reliability - Both platforms are reliable, but for the absolute worst conditions that can be imagined, I think the AK will run longer than an AR will. This is because of the gas system used in each rifle. The basic AR rifle "craps where it eats," in that it works on a gas impingement system to work the bolt. Hot gas and carbon are deposited directly onto the bolt during cycling, creating a dirty chamber and increasing the likelihood for feed failure. Most ARs will run fine IF you use good quality ammo and keep the bolt wet (lubed). An AK uses a piston system, and does not dump gas and carbon back onto the bolt. AK rifles have a reputation for reliablity for a reason. They just work.
Accuracy - AR platform rifles are generally more accurate. The degree of accuracy that you need is up to you. I've heard it said that the AR is a scalpel and the AK is a hatchet. Either is fine at close to medium range combat distances, but if you want to shoot holes in quarters at 100 yards, the AR is your rifle.
Which platform you end up choosing depends on what you plan on doing with it. If you plan to shoot a lot for enjoyment, maybe ring some steel and also have a rifle that would serve as an excellent defensive tool, get a basic AR and stock up on good brass case ammo. You can always add accessories later, like a red dot sight, rails, fancy grips, etc. You can even buy additional uppers in other calibers, making the AR platform the most versatile by far. Learn the rifle inside and out, and keep it clean. It will give you many years of excellent service.
If you just want to have a magazine fed combat style rifle for emergency defense and occasional practice and range fun, and you are on a budget, get an AK and stock up on good non-corrosive, steel case ammo like Golden Tiger or Silver Bear. A good AK has legendary reliability, ammo is cheaper and bigger bullets might make you more warm and fuzzy inside.
Here's a fun video to watch to help you with your research: https://www.youtube.com/watch?v=RuwR4LLvoc4
Initial cost - Talking about a basic, non-fancy rifle, you can pick up a Century WASR-10 AK, 2015 manufacture for about $600. I have one, and it is good quality. Some of the old WASR rifles that came into the US years ago were crap, but check the reviews for the new ones online. They are now decent quality rifles. Your basic AR can also be had for around $600, maybe a bit more. I have a S&W M&P15 Sport that I picked up a year ago for a little under $600. Works fine, I use decent quality brass cased ammo and haven't had a problem.
Ammo cost - AK ammo is cheaper. In bulk, 23 or 24 cents a round is a ballpark price. AR ammo is about 38 cents a round. You can get steel case AR ammo for about 28 cents a round, but some ARs will run it and some will not. More on that later.....
Ergonomics - This is subjective, but I like the feel of my AR better than my AK. The AR platform is a lot more modular, you can easily attach rails, foregrips, different stocks, etc to get it tailored just right. You can also do this to an AK, but there are not quite as many options due to the basic design of the rifle.
Reliability - Both platforms are reliable, but for the absolute worst conditions that can be imagined, I think the AK will run longer than an AR will. This is because of the gas system used in each rifle. The basic AR rifle "craps where it eats," in that it works on a gas impingement system to work the bolt. Hot gas and carbon are deposited directly onto the bolt during cycling, creating a dirty chamber and increasing the likelihood for feed failure. Most ARs will run fine IF you use good quality ammo and keep the bolt wet (lubed). An AK uses a piston system, and does not dump gas and carbon back onto the bolt. AK rifles have a reputation for reliablity for a reason. They just work.
Accuracy - AR platform rifles are generally more accurate. The degree of accuracy that you need is up to you. I've heard it said that the AR is a scalpel and the AK is a hatchet. Either is fine at close to medium range combat distances, but if you want to shoot holes in quarters at 100 yards, the AR is your rifle.
Which platform you end up choosing depends on what you plan on doing with it. If you plan to shoot a lot for enjoyment, maybe ring some steel and also have a rifle that would serve as an excellent defensive tool, get a basic AR and stock up on good brass case ammo. You can always add accessories later, like a red dot sight, rails, fancy grips, etc. You can even buy additional uppers in other calibers, making the AR platform the most versatile by far. Learn the rifle inside and out, and keep it clean. It will give you many years of excellent service.
If you just want to have a magazine fed combat style rifle for emergency defense and occasional practice and range fun, and you are on a budget, get an AK and stock up on good non-corrosive, steel case ammo like Golden Tiger or Silver Bear. A good AK has legendary reliability, ammo is cheaper and bigger bullets might make you more warm and fuzzy inside.
Here's a fun video to watch to help you with your research: https://www.youtube.com/watch?v=RuwR4LLvoc4
She's the best of both, baby!!! 
