LED is comparable to CFL in efficiency. CFLs usually have a warm up time. They come on and then get brighter. Often it's not noticeable but it can be annoying.
LEDs usually have a slight lag time from the time the switch is thrown, about 1/2 second on the latest one I bought.
CFLs are a lot cheaper and come in different color spectrums.
CFLs can be found for less $1 per bulb.
LEDs will cost you $15-25 per bulb.
CFLs are most efficient if turned on and left on for a time period. LEDs don't care how many times you turn them on and off.
You also have to be careful with LEDs because they often claim they are the same as a certain incandescent bulb when they actually are quite a bit dimmer. It's easy to find LED light bulbs online but they are often cheaply manufactured without the brightness they claim. If you stick with those sold by major resellers you should be OK.
I have used the following that I have purchased from Home Depot and am happy with the results. I am currently using one of each kind as will be using more as the CFLs I also am using start to fail.
Ecolight 6" 9.5 watt downlight (works in can lights)
Ecosmart 13watt A19
Phillips AmbientLED 12watt A19
EcoSmart 14-Watt (75W) Soft White (2700K) BR30 LED
One other thing about CFLs and LEDs. They lose brightness over time. The lifetime is not when they fail but when they have lost a certain percentage of their lumens.