Does enemy team gain solar when Ayla or Clunck kill themselves?

When you die:

For every death, no matter how you died (killed by droid, other awesomenaut, or suicide):

• You lose 30 solar.
• Each enemy receives 30 solar

So the above happens no matter what, every time you die. In addition to the above:

Killed by enemy awesomenaut:

• The killer receives 30 solar

Other deaths (droid, suicide, any other reason other than death to enemy awesomenaut)

• You drop 30 solar on the floor

So the total amount of solar up for grabs and lost by you is the same in all cases. It only differs in how it's distributed.
Meaning, it's better to not be killed by an enemy awesomenaut, because there is a chance that the 30 solar dropped on the ground can be picked up by teammates or left on the ground, rather than going straight to an enemy.
So suicide or dead by droid is a slightly better option. That's the only difference though.