The ships I have worked on all have incinerators but whether they are environmentally friendly or not who knows?
They still need fuel to burn the rubbish and the ash still has to be disposed of.
Are the amount of emissions from the fossil fuel used to burn the rubbish any better than landfill after you have recycled all you can?
For the vessels I work on it is a storage issue and disposal one more than anything which requires an incinerator as sometimes we don't get into port for months on end and only have supply vessels every now and then with limited space.
I would plump for the recycle all you possibly can but bin the rest.
Graham.