Hi Bigfoot,
The Chinese calibre is 5.8mm, not 5.58mm. Rim/body diameter is 10.5mm, compared with 10.0mm for the 5.45x39, 9.5mm for the 5.56x45, 11.3mm for the 7.62x39 and 6.5mm Grendel, and 10.6/7mm for the 6.8mm Rem.
The standard 5.8mm ball bullet is really an AP, with a long, hardened steel core - designed to go through body armour (it will penetrate 10mm armour plate at 300m). It is not so good at tumbling and doesn't fragment, so soft-target effectiveness isn't as good as the 5.56x45 (when that works as designed...).
The Chinese apparently decided on their own cartridge for reasons of national pride rather than anything else.