I tossed around the same idea a few months ago for my first AR. I ended up buying a complete rifle. I figured I could save maybe 100 bucks by building one, but I just didn't want to wait. I love my AR, but I regretted not building it myself, so when I bought my complete I took it home tore it apart and put it back together. that counts right?
Building a lower is pretty easy. I have never built an upper but it takes a few more specialized tools that might cut into your savings unless you plan on building multiples or taking it apart a lot. On the other hand a lot of manufactures let you customize quite a bit from the factory.
I bought one a few years ago, and I like it. But the one I built (the lower) a few months ago is my favorite, I know... shouldn't have favorites...
I built the lower and found an upper that I liked.
You might want to look around at uppers, and make sure they're in stock, to see if you find one that you like. That's the nice thing about ARs, you can swap uppers and you have a new gun.
Lowers take some simple tools to put together. Uppers, unless you guy them barrelled, will take a vice and an upper assembly holder. It's cool to build one exactly how you want it and have it actually work.
Not to be a grouch, but what you are asking has been beaten to death and past purgatory. There isn't much that beats doing your own research.
That said, before you ask that question--even to yourself--you need to identify the purpose(s) for this firearm. From there, you will be at a much better position to decide what which is better. For example, if you need a defense carbine, you might be better off buying complete receivers from reputable manufacturers as "parts are not parts". If you need a precision rifle for recreation, you might find a wider variety of after market parts to suit that purpose, so building your own may be the better option.