Maybe the original installer wasn't planning to run enough stuff off the inverter to need a bigger breaker so maybe that's why the 120a.
Fuses/breakers are to protect the wire, so the biggest you can use is however many amps the wire is rated to handle.
Even if the inverter could do 6000w, that'd be more than the wire is rated for, so you don't size the breaker based on the inverter's rating, but only based on the wire size.
I had continued to research and forgot to update my post with my wire ratings and what I was finding. What I'm gathering is that 2/0 awg wire (aka "00" wire) with a 105*C insulation rating for a 25' length can handle somewhere in the neighborhood of 195A. I've found other sites that claim it can handle up to 300-400A but the majority of info I'm finding is in the 200A range. I need to pull all of the info off of the wire to see if I can pin this down more. It definitely looks like 2/0 awg industrial welding cable.
http://www.powerstream.com/Wire_Size.htm
http://en.wikipedia.org/wiki/American_wire_gauge
Then I found this link that is more specific to 12v systems and it claims 100-150A:
http://www.alternatorparts.com/wire_size_chart.htm
I'm thinking 150A breakers throughout the system is probably the biggest I can go.
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