The Barnes 62gr TSX and 70gr TSX are known to work well on game, and I’ve heard unsubstantiated claims that two legged upright vermin are suitably smited by them as well. I know that out of my 1:7” twist cold hammer forged chrome lined 16” Knight’s Armament SR-15 E3 Mod 2 that the 70gr Barnes stabilizes just fine and gives 5 shot groups of 1.25”-1.5” at 100 yards using a 4X optic that is not optimized for shooting groups.
Downsides are cost, and over penetration concerns since they are all copper. Also note that the 5.56mm 70gr TSX load is reported to be pretty hot, and they’re not kidding about the warning to run it in 5.56mm NATO chambers. A friend of mine bought some to run in his 1:8” Rock River with a .223 Wylde chamber: it flattened primers, and had signs of brass flow into the ejector with nasty extractor swipes on the rim. The 1:8” twist also didn’t stabilize the bullet well enough to give good accuracy, his groups were around 5”-6” at 100 yards. My carbine shot it well, ejected brass into a nice consistent area, and the brass looks like it came out of a bolt gun. I bought the rest of his supply of this ammo, and he tried the 62gr TSX 5.56mm load and it worked great, including visual pressure signs on his brass. I suspect his chamber is too tight, and the throat is too short, and the long (longer than a 77gr SMK!) all copper 70gr bullet was jacking pressures up at full 5.56mm NATO loading.
Also worth a look is the FBI carbine duty load, Federal XM556SBCT3 (62gr bonded core). It meets all their criterion for barriers, expansion, penetration etc. Not sure how available it is to non LEO buyers though.