Benefits of a single phase inverter on a 3 phase supply:
- $200-$400 cheaper
- Easier to add a battery system later which can charge the batteries from the solar in the event of a black out (only an issue if you are worried about getting a battery in the future and you want the battery to recharge during long grid outages).
Benefits of a 3 phase inverter on a 3 phase supply:
A 3 phase inverter across three phases results in more stable operation, with less voltage and frequency swings and less tripping off of the inverter. If the inverter trips you lose all your solar generation until the inverter is manually or automatically reset. In other words your 3 phase inverter is much less likely than a single phase inverter to trip off on 'over voltage' or 'out of frequency' faults, which is becoming more of an issue as more solar is connected to the grid.
Although 3-phase inverters are more expensive than single-phase inverters I personally believe their benefits outweigh the extra cost (expect to pay about $500 extra for a 3 phase 5kW inverter compared to a 5kW single phase inverter). But then I'm not worried about extended grid outages and surviving the ensuing Zombie Apocalypse.