- La Niña seasons:11.8/6.8/3.2
- Neutral seasons:11.7/6.9/2.9
- El Niño seasons:9.0/4.8/1.9
As you can see there is no big difference between La Niña and Neutral seasons but during El Niño the activity is reduced.
Now the activity depending on the strength of La Niña:
- Weak La Niña (from -0.5°C to -1.0°C): 11.7/6.2/2.7
- Moderate La Niña (from -1.0°C to -1.5°C):12.6/7.4/3.4
- Strong La Niña (>1.5°C):10.8/6.8/3.6
As you can see moderate La Niñas have more tropical storms and more hurricanes than strong or weak La Niñas.
Activity depending on the strength of El Niño:
- Weak El Niño (from 0.5°C to 1.0°C):11.8/8.0/3.8
- Moderate El Niño (from 1.0°C to 1.5°C):8.0/4.8/1.0
- Strong El Niño (from 1.5°C) : 8.0/3.3/1.3
In this case you can see that weak EL Niños are very active and produce more major hurricanes that any other ENSO phase

Now the activity depending on the phase of the AMO and the phase of the ENSO.
Cold AMO (1970-1994):
- La Niña:10.6/5.3/2.1
- Neutral:10.4/5.9/1.7
- El Niño:7.3/3.8/0.9
During the cold phase of the AMO La Niña years have slightly more tropical storms and major hurricanes and El Niño years have much less activity than Neutral and La Niñas.
Warm AMO (1995-2009):
- La Niña:15.0/8.6/3.6
- Neutral:17.8/9.8/5.0
- El Niño:10.8/4.8/2.6
In the warm phase of the AMO Neutral years have had more activity than La Niña years (maybe 2005's fault) and El Niño seasons again have less activity.
I know that this statistics may not be the best way to conclude wich seasons are more active but anyways they are very interesting.