Efficiency difference of an evaporative air cooler based on its dimensions (wider or taller) given that all the other aspects are same

I own an evaporative air cooler of width 28 inches and height 34 inches, I was wondering if a taller air cooler with lesser width (but same surface area as the one I own) would have been more efficient in cooling the room.

My logic is that a cooler with lesser height would throw the air at a lower height and as cool air tends to sink, taller coolers can be more efficient. But also my bed rests lower on the ground so a cooler with more width and lesser height would throw the cool air horizontally (which would be better) while lowering the direction of the taller cooler would result in throwing the air at a negative angle from the horizontal which intuitively feels to me that more cold air is lost as its basically cooling the ground more.

How do I calculate the difference in efficiency of both the coolers given their surface area and all other factors are same, at different levels of height in the room. Assuming the fan is not turned on i.e there is minimal vertical air flow. What all criteria should be taken into account? How would it affect the calculations if the fan is in fact turned on i.e more vertical air flow?