The specs for the Honda eu1000i
suggest that the smaller units is only slightly quieter under the same conditions... and that an eu2000i at idle (53 dBA?) is significantly quieter than an eu1000i at full load (57 dBA?). I wouldn't be surprised to find that Bob is correct and in actual use at a few hundred watts output the bigger one is quieter. This applies only in Eco (variable speed) mode; the same would apply to other brands.
I think the roughly 2000 watt size is very common, so it will be a better deal than the more obscure little (600 to 1000 watt) size... plus, some things don't scale well and so an engine half the size will always cost more than half as much. Still, the smaller unit may make more sense for some people, depending on what they can lift, carry, or store in their trailer or tow vehicle.
The Yamaha EF1000IS specs
look pretty similar to those of the Honda eu1000i. As Bob said a few days ago, I don't see a current 600 watt model from Yamaha (or Honda).