If we’re talking AR vs M4 or M16, there’s not a lot of difference. In fact, I’d lean towards saying that in some instances civilian weapons might be better than military weapons. And I would definitely take a civilian long range bolt rifle over pretty much anything in the conventional military for that purpose.
That said, there’s a whole lot of other stuff that goes into fighting than who has the better gun. Small unit tactics is about the highest level of warfare that civilians can expect to compete against any sort of real military, be it US or foreign, without external aid (other countries giving us weapons), and even that’s a stretch. We don’t even have the ability to match an infantry company - no anti-armor ability or indirect fire (mortars). And that doesn’t even get into mobility issues like being able to deploy by helicopter.
Looking at just firearms, there is a pretty big gap due to the lack of belt fed machine guns. Four or five guys with ARs can probably have the same effective suppression of an area as one belt fed for a short amount of time, but it’s going to be difficult to keep that up for say, 3-5 minutes while your other team maneuvers on the target.
The largest issue in my opinion is that while lots of us know how to manipulate our firearms, few of us actually know (and practice) how to fight with firearms as individuals, and even fewer actually know how to fight with firearms in groups. For example, when was the last time you and your friends practiced fire and maneuver, bounding overwatch, or setting up an ambush? How many of us can effectively fight at night? Who has night vision and the training to use it?
For an even simpler measure, how many of us can put on a fighting load of armor + mags, rifle, pistol, and then whatever gear you need to live in the woods (hiking gear) and then walk a mile?
Not saying that everybody has to do that (everybody has their own interests) but there is a whole lot to effectively fighting as a group, and knowing how to shoot a gun and hit a target is only a very small part of it.
Point being that even if I had desire for something akin to an abrams tank, the cost to buy it, drive it, and shoot it is as much or bigger issue than the legal hurdles that might be in place.
Technically if you can find someone to sell you an Abrams, you can buy it. I don’t think I’ve seen an Abrams for private sale, but there are definitely a lot of older tanks and APCs that are relatively available. If memory serves, you can get a Soviet APC for the price of a new Honda Accord. Though to be fair, it will cost a bit to ship it over here.
The weird thing is that if you do buy a tank, you can reactivate the main cannon by just paying $200 and registering it as a destructive device, but the coaxial machine gun has to be transferable (unless you’re a SOT). So your supporting machine gun is effectively more heavily regulated than the main gun.