Gensets & AC
Marty makes some good points, the guy I saw last summer was using a 5000 BTU window unit hung in his companionway (I think he bought it from a brandsmart). I have heard the 2000 will not do a 6000 BTU unit and you might consider checking around to places that sell both Honda generators and AC units (Shell lumber in Miami) for advice from folks who have customers using the units for a week or two after a hurricane. Honda makes a harness where you can connect 2 generators together to double the rating. If you are thinking of doing a full - on Marine installation for your AC, I know Dometic has some low -draw staged start -up units that can run on smaller generators.
I have a diesel auxillary engine below deck on a sailboat and I keep my gasoline for the outboard and generator on deck - safest practice as gasoline vapors are heavier than air and can settle into a bilge forming a potentially explosive situation. Things may be different on boats powered with a main gasoline engine(s) where a good deal of ventilation (big blowers etc) are built into their design.
As far as 1000w to 2000w comparisons go I think the footprint for the 2000 is roughly the same as the 1000 with just a few additional inches and pounds for weight. These things sip gasoline so if you don't mind the expense of a few more ounces a day and another $200 for purchasing then get the 2000 - we full-time cruise and it is soooo nice to charge batteries / make ice / surf internet or watch TV without worrying about "tripping" a small generator. We loved our old Honda 1000 (there wasn't a "suitcase 2000 when we bought the 1000), but I don't understand how they are still able to sell them after the 2000 has come out. If the space you are planning to keep the generator is so tight that you have to go 1000 then get it and plan plan plan your power management otherwise live fat - be happy.....given the choice between a free 1000 and a retail cost 2000 I will take the 2000 every time.