To an extent, I agree with chaser. All milspec is, is a minimum set of standards that have to be met; however, there are many rifles out there that do not meet the minimum standards.
What makes a rifle top tier is the materials that go into the parts that make up the rifle. Heck, a year or so ago, I ran across what I thought was a really good deal on receivers, but upon reading the fine print, discovered that they were milled from 6061 rather than 7075. Still, the barrel, trigger and BCG are the heart of any AR and I prefer that they meet milspec at the very least.
Non milspec or lower to mid tier rifles often have barrels, BCGs and/ trigger groups made of inferior steel. To get the better materials used in upper tiers rifles costs more money, so the question then becomes one of whether you will use the rifle enough to actually realize the benefits of getting an upper or top tier rifle.
The barrel for instance. Barrels made of inferior steel will in all likelihood shoot just fine for most, but for someone that runs one hard, it may mean that they will burn the barrel out sooner, or that accuracy will suffer more when the barrel gets really hot. One thing that I consider to be pretty important is that a milspec barrel will be coated in the area under the gas block. Most non milspec barrels are not. Although this may not sound like it's important, it could be for you if you live or use the rifle in a harsh environment and then one day you are cleaning your rifle and wonder what the ring of rust is around your barrel at the gas block.
Another problem I've seen more in non milspec barrels or more specifically lower tier rifles is that the gas ports are too big. I think that some manufacturers do this to lend some reliability to a rifle and it does work. The problem is that over time, an over gassed rifle will beat the heck out of itself and may also pose some problems shooting steel cased ammo.
A non milspec BCG may not last as long as a milspec BCG due to inferior materials and/or lack of testing. I say MAY not, because I've had cheap bolts that I got from God knows where go a good 6000 rounds before they lost a lug.
As far as triggers go, I don't know. I run Geissele triggers in all of my ARs and consider them to be superior to milspec; but I do know that there are some popular two stage triggers out there, like the Rock River that lots of guys say they love. The trigger is nice and feels pretty good, but I've seen more than a few go south when they hit around the 3000 round mark; although I think that RRA may have fixed this problem. I don't know, I quit using them.
If you really want to see the advantages of a top tier rifle, take a carbine course and take note of the rifles that the others guys are using and then take note of which ones it is that choke during the course.
This is, of course, just my opinion. I'm not a soldier that's been to war, nor am I a part of any special law enforcement team, but over the course of tens of thousands of rounds through ARs, I kind of got a feel for what keeps running and what needs replacing sooner than it should.
Still, in spite of all of this, get what floats your boat. If you take owning an AR seriously and learn the rifle, odds are that you can keep the biggest piece of crap on the market running the way it should. If you get a top tier rifle, odds are that it will run longer on what it came with before you need to start replacing stuff. A cheap rifle is more of a roll of the dice.
To be honest, most of the problems that I've seen with lesser tier rifles has been really stupid stuff. Like gas rings wearing out prematurely or defective extractor springs and extractors. Weak ejector springs and buffer springs and such. Some more serious problems I've seen are trigger groups that lack the proper hardening and actually thrill the owner with how nice they get while breaking in, all the way up to the point where they go full auto; or out of spec chambers.
If you want to dip your toe in the AR pool and don't want to spend a lot of money, the Smith Sport may be for you. They cut a few corners with the rifle. 4140 steel for the barrel, an integrated trigger guard, no dust cover and no forward assist, if you care about those things. The rifles do shoot well for the price. I really can't tell you how they would fare in the long run though. I don't know anyone that has 10,000 rounds through one yet.
I know that there have been and likely will be more recommendations for the Smith and Wesson and I have to assume that the Sport is what they're talking about, because Smith's "better" models aren't cheap and at those prices, there are definitely better options.
If you are willing to spend the money, for around $1000 you can start considering some really nice rifles that are probably less likely to let you down; but like I said, if you really get to know the platform, you can keep just about anything running.
ARs are like tinker toys. There isn't a single part that I can't change, including the barrel, in 30 minutes or less. My AR is a franken rifle. I had gotten out of ARs for awhile and one day while digging through my parts bin, realized that I had enough parts to build a rifle. I try to keep up with the maintenance, but once in a while something gets by me. If the rifle stops running, I just change whatever it was that made it stop. The only part I'm kind of particular about is the bolt/carrier group. I run a Bravo Company group and keep a spare bolt in my grip. Although I have been surprised by some "lesser" bolts, I've also seen some that gave up the ghost a little too quickly.
Would I buy a top tier rifle, like a Noveske? i don't think so. Not unless I run into a guy that was really hard up for rent money and I can practically steal it from him. If I bought a rifle, it would probably be a solid upper mid tier rifle, like a Bravo Company or maybe a Daniel Defense.