There are a lot of questions surrounding AR-15’s these days. What caliber, what brand, what barrel length, what color? These are just some of the simplest questions you can ask concerning an AR-15. The only question that needn’t be asked is whether or not to have an AR-15. We already know the answer to that question. There is another question that is very important though, when it comes to this particular medium of firearm, whether to build or buy? Though this question is quite subjective, there are some generalities we can observe that may help you personally answer this for yourself. 
     The build or buy question has an obvious answer if you know exactly what you want. That answer varies widely depending on who you ask. There are compelling reasons for either side and the decision that you might come to today could be quite different tomorrow. It might just depend on what’s on sale, or how quickly you want to get that sweet AR-15 into your hands. You might be looking for a fun project to work on or want the peace of mind that your rifle was put together by professionals. There is a kind of middle ground in the build/buy debate, a kind of compromise and it can be a great way to go. The idea is to get a complete upper set and a complete lower set. Once you have the two complete pieces, attach them at the takedown and pivot pins, and now you have a complete AR-15. That’s it, simple, easy, straightforward, and possibly very inexpensive. 
     It should be noted that unless you somehow have free access to a bunch of gun parts you will still be buying what you are building. However, building does tend to be less expensive than buying. Buying is convenient and fast. It gets that completed gun in your hand as quickly as possible. However, is it actually complete, as in every component of the firearm existing harmoniously and possessing all of the qualities that you think they should? 
     To simplify, here is a breakdown of the reasons for build or buy. This is likely not all of the reasons, but it covers the more common concerns.

Why Buy: 

- Super easy and convenient 
- Guaranteed to work (or should be anyway, at least you won’t be the one that screwed it up) 
- Often guaranteed to work for a while, usually years 
- Ready to go right away, just load and shoot 
- Made with compatible parts(incompatible parts might work with each other, just not as well. Then again incompatible parts might be dangerous to have in your firearm.) 

Why Build: 

- Customization 
- You get exactly what you want (or at least know exactly what you’re getting) 
- Can be almost like buying it on a payment plan 
- Generally less expensive 
- It can be a fun project (find out why it’s called "Adult Legos") 
- Better knowledge of how your firearm works 
- Aforementioned knowledge will assist you if something goes wrong, know which part needs to be replaced 

Some Cons of Buying:

- Inverse to Why to Build ie: initially not as customized, might get something you’re not as stoked to have, paying all at once, might get to read a boring manual instead of putting it together yourself. 
- Generally a bit more expensive 

Some Cons of Building: 

- Not as Guaranteed (if it doesn’t work, you're the one to blame) 
- Sights are not set at all, you need to zero them yourself 
- Gotta know yer stuff (which can turn you into a pro once you do) 
- Extra effort (which can also turn you into a pro depending on how much you enjoy it) 

     As you can see there are many different reasons to go either way. It is a very personal and situational decision. More control or more convenience, saving money or getting what you want, do it yourself or leave it to the experts. The best part about all of this is that there are no wrong answers. You decide what is important for you and proceed accordingly. If only every question in life had such great answers!