the Champions don't have as much power as the Honda 2000 but they'll work fine.
don't see much reason other than long term reliability. Honda's rep is well-established while Champion inverter 2000w has only been around a couple of years. Champion does have a great rep for customer service and their 3500 open-framed one does have a good rep for reliability.
and Zoe the Wonder Dog(R.I.P.)
'07 Roo 23SS pushing an '07 Chevy Avalanche
Equalizer WDH and Prodigy BC