Indeed, there are noisy 2-stroke engines and quieter ones. The one I listed in my previous post is 60dB at 22 feet whereas the the Honda EU 2000i is 59dB at 23 feet. I'd still rather have my Honda.
Indeed,I am not getting rid of either of my Honda's(2K&3K) either but for someone like the opp who just wants a cheap generator to charge his batteries,the one I listed would do a great job and quietly.In our case,it's a plus it uses the same mix as our Stihl chain saws which is on hand as much as regular gas at our house.
I chose the Honda 2K for my needs and running sensitive stuff quietly but everyone's needs are different.The two stroke fills some peoples needs while the four stroke fills others.In either two or four stroke you must do your homework before buying and choose what works best for your application.
This GEN1250 two stroke would have been a good choice with my Lance camper to charge the battery.Small/light and quiet for a generator.