The 430EX III-RT is almost exactly a half 600EX-RT. Half power, half weight, half size, half price.
Compared to the 430EX II it is improved in almost every area, especially when it comes to interfaces (wireless and buttons/display).
The main disadvantages compared to the 600EX-RT are less maximum light output and slower recharge at same light output (at full blast the 430EX III recharges slightly faster than the 600EX-RT but at half the output). And the much smaller flash head (especially the extremely small free space on the low side when it is pointed forwards) makes it difficult to attach larger flash formers like soft boxes.
The main applications I see, are:
1. when weight, size and price is more important than power
2. as a replacement for a ST-E3-RT (to get fill flash and AF assist) or for a 600EX-RT (for price, weight and size reasons) as a transmitter
3. to be able to distribute flashes (compared to half the number of 600EX-RT) more evenly with the same total light output for the same price when using multiple flashes to light a room