Unfortunately, the little Champion inverter won't start a lot of loads that the Honda eu2000i can handle easily.
I returned one of these after it wouldn't start an A/C unit or any power tools that have a high current draw at startup (miter saw, air compressor, etc.).
The Honda handled them all with ease. The Honda is also smaller and lighter and retains some resale value. Depending on where you live, you can probably find a used Honda in mint condition for around $700.
Here's an example on youtube:
https://www.youtube.com/watch?v=WyB3w_tJxYY