In terms of sail-boat efficiency of rig, there are really two competing factors: 
 manoueveravbility/manageability and power.
Most designs are optimized for a particular trade-off between these two.
There are two main types of design:
 square-rigged or fore-and-aft rigged
And there are three main types of sail:
 rectangular, quadrilateral or triangular/lateen
Generally speaking, square-rigged ships only (built for size, power and endurance), have mainly rectangular sails, while the other
 shapes of sail are found on fore-and-aft rigged boats (built for smaller size, acceleration and manoueverability)

With regard to power, the golden rule is that the more wind is caught and held by the sail(s) the greater the force moving the boat.
Therefore with regard to power, there are three main factors varying with the above types of design:
1) angle to the wind - the closer the sail(s) stay to right-angles to the wind the greater the power
 - as is more the case with square-rigs over fore-and-aft rigs
2) shape - the closer the sail is in shape to a circle, the greater the catchment of wind per unit area of sail
 - as is more the case with square, then quadrilateral, over triangular, sails
3) fullness - the more concave the sail, the greater the amount of wind held, and thus the greater the power
 - as is most the case with a spinnaker/ballooner, then square, quadrilateral, and finally triangular sails

With regard to manoueverability/manageability, the most important considerations are ease of tacking,
 speed of variation of the amount of sail exposed to the wind, and size of crew needed for operaion:
1) tacking - mounting the sail(s) on a movable boom (for triangular sails) or gaff (for quadrilateral sails) makes tacking practical
 for fore-and-aft rigged boats, unlike square-rigged ships.
2) shape - triangular sails, because they hold less wind, are usually quicker and easier to reef
3) fullness - again, triangular sails are easier to reef (except the very full, specialized, but triangular, spinnaker)
4) angle to the wind - if the sail is on a boom or gaff, i.e. not at right-angles to the wind, the easier to alter or reef 
(because of holding less wind) and hence the smaller the crew needed