Partly this depends on exactly how you wash the reusable ones, and how often. If all you had in it was some coffee, and for a few cycles you just rinse thoroughly but quickly with very hot water, rather than washing with soap, I suspect the amount of water and energy involved is not bad. Really, if there's nothing dried on, you don't need a full wash every time. Heat will reduce the viscosity of any oils enough to get most of it off, and obviously hot water is great for removing sugars... Oil will gradually build up on a plastic cup, because oils bind to plastics, so you do need to wash eventually -- say, once a week, or any time that stuff actually gets dried on.

If I use my beloved Cafe Q cup and I finish the drink while I'm still out far away from a sink, I try to at least get some water to pour in, then I seal it up and shake it a bit, to keep the inside moist, so stuff doesn't dry on...