My experiences with these generators:
I have owned a Yamaha YG2800i. This is identical to the EF2800i except that the YG2800i comes with a GFI 20 amp duplex receptacle instead of one that does not have the GFI protection. I purchased mine from USA Light and Electric and received great service and a great price. They can be found at:
http://www.yamahagenerators.com/
This generator worked well with our 32 foot Holiday Rambler travel trailer. It ran the air conditioner and everything else we used. I did not attempt to run the a/c and the microwave at the same time. Running the a/c in July in the Washington, DC, area would empty the 3 gallon tank in about 20-24 hours. At more normal loads, a full tank will run that generator for a couple of days easily.
When we got the 34 foot Airstream, with its 13,500 BTU air conditioner, we found that the Yamaha would not start the a/c. I didn't think that the a/c on the Airstream was any larger than the one on the Holiday Rambler, but I guess it is.
The Yamaha was quiet enough to run it constantly at a dog show with no complaints from any neighbors. It didn't bother us inside the trailer either.
I haven't owned any of the Hondas, but I heard a number of them running at a lumber products show I attended recently. The Honda EU3000 units were so quiet that I couldn't tell they were running until I was standing beside them. Often I could hear a generator running in the distance as I walked through the RV parking area and didn't know that the Honda EU3000 that was 15 feet away was also running. I would have to be within 15-10 feet of the generator before I realized it was on. This was with normal daytime noises in the RV parking. No one was running a chain saw in this area. I'm sure at night, the generator noise would be more easily heard, but I would not find it offensive. Every owner I talked to loved it.
There were a few of the Honda EU2000 generators there, but not enough for me to form an opinion on them. If I were in the market for a generator again, I would buy a pair of the EU2000 units plus the parallel adaptor. This would allow me to run the Airstream's air conditioning with both units, or to use just one when the load didn't require maximum power. They are also much easier to handle, as stated above. The price for two EU2000's is about the same as the price for a single higher-power unit.
Yamaha is now making the EF3000iSEB. This unit uses the starting battery to add to the generator's output to provide a power boost when required. It's supposedly very quiet. The drawback to it is that it's heavy and expensive. It's available here:
http://www.yamahagenerators.com/ef3000iseb.htm?cart=10984178121699161
If you are curious, I am now running an Onan MicroLite 4000. The reason for this is because we already owned it. I had never gotten around to building a cart for it because the Yamaha was so handy. When the Yamaha wouldn't pull the load for the Airstream I dusted off the Onan. It's a nice unit that has plenty of power. It's also surprisingly quiet, but it's also big and heavy. The main thing in its favor is that it's paid for.
The bottom line: If the Yamaha will do the job for you, buy it. It's a nice, compact, economical, quiet generator that's light enough to lift. If you get the Yamaha, buy the YG2800i, not the EF2800i. If that's not enough generator, try the big Honda or two small Hondas in parallel.
Loren