What Honda? The 3000 watt inverter gen. is usually only about $1,800.
An inverter genenerator will produce extremely clean power, run quieter, and use less fuel than a non inverter generator under most conditions. It will also cost more as you've found.
If your just running construction tools or the air conditioning than any old generator will do. If you're running computers, TV, Sat., DVD, etc. I would want the cleaner power of an inverter unit.
If I'm camping next to you I will greatly appreciate the lower noise of an inverter unit.
A Honda generator, inverter or not, will likely outlast any other generator you can buy.