To me the difference is that Permaculture extends beyond agriculture (housing, community structure, energy production etc.), and there is more emphasis on perennials and tree crops than ecoagriculture. Though I'm not too familiar with the ecoagriculture term.
Also not familiar with exactly what 'natural' farming is, but permaculture stresses observing nature and using it. The One Straw Revolution by Fukokua is one thing that comes to mind when thinking about 'natural' farming, and that book is rather popular among permies.
Usually, when I describe permaculture to people in agriculture, they say 'Oh, agroforestry!" But I think most conventional agroforestry is more geared to monoculture and it often ignores some things that permaculture finds important, like linking up different species to perform different ecological functions, using multiple canopies/trophic levels, using place appropriate solutions, etc.
Also, permaculture has a strong social and ethical component that could be part of any system of agriculture, but it is only in permaculture that this system is consistently taught.
I think permaculture is more a sub-division of ecoagriculture. Ecoagriculture is called such because it is ecological and economical. It is more encompassing, it abhors herbicides and pesticides, chemical fertilizers are all right, monsanto is hated, etc. I am more ecoagriculture, with permaculture mixed in. I'd rather not use chemical fertilizers, but they aren't poisons. However, we do rotational grazing systems (getting it set up), and multi-species grazing, which is rather permaculture. So, they are rather mixed, I guess
Well, I'm not quite sure what exactly permaculture is yet, but permaculture and ecoagriculture and very similar. No, I was not saying permaculture was not economical, I don't know where you got that, in fact it can be very economical if done right.