Charging the battery with a generator: AC or DC?

I have been reading some of the old threads on batteries and generators. I am interested in getting a generator for charging the battery during dry camping. We have a trip out west planned for this summer, but most of our camping is in the east where most campgrounds tend to be in shady areas (making solar not practical). The Honda EU series looks like a reasonable choice for low weight and low noise. How long will it take to recharge the TM battery with a generator with either the EU1000 or the EU2000? (With minimal load). - Bob