Check out this group I fired tonight at 100 yards with my Dad's old Remington 700 Varmint Special with Leupold 6.5-20x40 Target scope. Those 3 shots measure 0.067" center to center. Calipers pictured show 0.375 outside to outside. This old rifle and cartridge can still shoot some incredible groups. This is my personal best group I've ever shot at 100 yards!
.308 Winchester
168gr AMAX
43.6gr Varget
Remington 9 1/2 Primer
2.875 OAL
Peterson .308 Win Match brass!
I wouldn't say the 308 still has it, I would say the 308 will always have it.
It is known for being deadly accurate, reason why it is still around and will always be around