Gen III is just another name for an LS1.
Gen III refers to the fact that it is the third generation small block chevy V8. LS1 is an engineering codename.
Although technically after the VT model the engine spec is actually an LS6 - which is just an LS1 with some very minor differences, notably the inlet manifold being better. The LS6 tag very rarely gets used though. The "LS1" lasted up until 2004 when the 6.0 Litre LS2 took over in the HSV's and in 2005 the Holden's started using 6.0 Litre L76 engines and then later L98 engines.
There are very slight differences to the cam specs across all the years models. None of the factory cams would be notably better than any aftermarket cam though due to the factory cams low lift properties, small duration and large Lobe separation angle (all of which are not condusive to making power)
The best normally available ( ie not the 7.0 Litre LS7 and 6.3 Litre HSV LS3) LS series engine would be the 6.0 Litre L98 used in the current VE holden SS's. They have very good flowing heads from the factory and are slightly better than the older LS2 6.0 litre because of this - especially when modifying them with aftermarket cams.