All air conditioners have a passage for room air to flow into the unit, flow over the cold side of the compressor coil and return to the room. This both cools the air and condenses some of the moisture out of the room air, which makes the room dryer, more comfortable and easier to cool. With full house air conditioners, split ductless air conditioners or those that literally stick out the window, the hot side of the compressor coil is sitting outdoors. Outdoor air, at whatever temperature, flows over these coils to cool them down -- completing the action of extracting heat from inside the house. Of course the cooler this air is outdoors, the more efficient the air conditioning.
Portable air conditioners sit totally inside the room. This means that the hot coils of the compressor are also inside the room (the hot side is outdoors with all other air conditioners), which makes them inherently inefficient - you have to cool the space that they heat, kind of like fighting against itself. So from an energy conservation point of view I cannot recommend these units at all, but if you really need the portability or don't have good options for a window air conditioner (like casement windows), a unit with a hose like duct to the outdoors may be your only alternative. Now the question comes: is the unit with one hose or the unit with two hoses more efficient?
There is definitely a difference but not a clear winner.
One hose units will take a small quantity of the cooled indoor air flowing through the unit and divert it over the hot coil and out of the room through that exhaust hose. This has the positive effect of running air over the hot coil that is cooler than outdoor air, increasing efficiency. But because air is being exhausted out of the room, more air will flow into the room that now needs to be cooled and if this air is humid, the higher humidity will make the unit less efficient. Back on the positive side, this unit will create a bit of a change of air in the room, making it less stuffy.
Two hose units use one hose to bring outdoor air into the machine, run that air over the hot coil and then the other hose to throw it back outside. This machine essentially works more like all other air conditioners where indoor and outdoor air streams are independent. This means that the action of the portable air conditioner will not create a negative pressure in the room, and will not create any air change in the room -- no hot fresh air coming in, no new humidity either. If the air in the room is stuffy or polluted, it will now be just as stuffy and just as polluted but less humid and cooler. The two hose unit will be less efficient because it is always using warmer outdoor air to cool the hot compressor coil but more efficient because there will be no new humidity drawn into the room. It looses a bit on the efficiency side because it has two fans rather than one.
Professionals tent to feel that it is a draw between the two technologies. If there is a winner it might be regional -- two hose units winning where outdoor humidity is very high and one hose units winning where the air is relatively dry but hot and no winner in-between.
That's the best I can make of it -- Jon.