I have two Champions AND I just bought my second Powerhouse. They are both great options.
Champion is going to have better reliability out-of-the-box, and better customer support. Powerhouse has better design and engineering, the best in the industry by far. I own the Champion 3500, Champion 1200 (retired), the Powerhouse 2600/2700, and now the Powerhouse 450/500 (yes, that's a 500-watt gennie).
My personal recommendation is the Powerhouse 2600/2700 inverter gennie, for around $1,000. This is equivilent in power to the Honda 3000 for about half the price. It is MUCH lighter (almost half the weight), and it is parallelable. The Powerhouse 2100 is also parallelable, but not the 2000 you linked to.
When I bought my first Champion gennie, there were people on this forum talking about vandalizing or even shooting them--that's how open minded they can be. Now of course, Champion is a respected brand here, but powerhouse is labelled "Chinese junk". In time Powerhouse will be appreciated for what they do really well, which is design uniquely capable generators, and the vandals will have to figure out something else to target..