I am just about to finish building my first AR so hopefully I can share a couple things I learned and also why I chose to build vs. buy.
If you buy a complete rifle you're going to pay an extra 11% excise tax (Pittman-Robertson Act) right off the bat which is built into the price of the rifle vs. if you bought the same rifle upper and lower and simply ''clicked" them together. Now don't get me wrong this excise tax money does good things and goes into the U.S. Fish and Wildlife Services, but if you're on a budget like me then every dollar counts... On a $1,000 rifle that's $110 bucks you could be spending on something else like optics or new furniture.
If you buy a complete rifle you're likely going to want to change somethings about it like the grip, stock, charging handle, hand guards or sights/optics... so plan that into your overall budget.
I ran the numbers and I think it's worthwhile to buy a stripped lower receiver and assemble it yourself, there seems to be a definite cost savings from my research.
The upper is where it gets tricky, I wanted some specific things in my upper. I had a hard-on for a cold hammer forged barrel (CHF), I wanted mid-length gas system and I wanted a government profile and I really couldn't find much in stock anywhere matching what I wanted. I found a couple complete uppers that were close (CHF barrel w/ mid-length gas but lightweight profile barrel). So I ran the number on buying a stripped or even completed upper receiver, a barrel, bcg, etc and building it myself and it just didn't make sense financially to build my own as I didn't appear to be saving much if anything at all. Plus on top of a break-even or maybe paying a bit more for what I actually wanted I'd have to assemble it and I was kinda worried I'd end up going to a gun smith anyways if I needed a special tool or if I jacked something up. In the end I found a complete upper from BCM that fit what I wanted but it was about $100 more than I was hoping to spend, however it wasn't any more expensive than if I tried built it myself so... Also as stated on BCM's product page "Prior to shipping, all BCM® upper receiver groups are test fired for function, laser bore sighted with a Milspec carry handle for sight alignment within Mil-Specs, and then batch samples are test fired for accuracy." Now I'm not saying buy this brand or buy that brand but what I am saying is I personally think there is a piece of mind in buying a completed upper that's been test fired and laser bore sighted prior to shipping it to you, at least there was to me.
So was it really cheaper to build vs. buy? As it stands my AR15 when complete should come in at just under/over $1,000 (last two things I need to buy are hand guards and a rear sight). Now there are obviously lots of good options out there for complete rifles for under $1,000 but I'd like to think for that for my $1,000 I got real top notch quality parts and also everything on my wish list - CHF barrel, FDE magpul moe furniture, BCM gunfighter charging handle and a lower receiver with the the punisher skull on it

I ran the numbers and if I were to buy a complete rifle with everything I wanted I think I'd be looking at about $250-500 more than what I spent building mine. So I do think there was some cost savings for me personally, however for me building vs. buying was really more about getting what I wanted.