Takemikazuchi
Summon effect is far more useful in typical situations
Passive is also usually better except for when one has low assault. And in the cases when one wants a +assault eidolon, one prefers a 40% assault/20% HP eidolon. The +20% to burst streak passive doesn't do much*

*It's not an increase to burst damage, it's specifically an increase to burst streak damage.
Burst streak damage is a percentage of the sum of burst attack damage dealt that turn, if more than 1 character bursted.
If it is a full burst, burst streak is 50% of that damage.
+20% to burst streak would turn that 50% to (50%*1.2) = 60%, ie an increase of 10% of the sum of burst damage.

For a baseline example, let's say that everyone involved is a 3* SR, including the soul wielding a 3* SR weapon. Each person's burst is then basically 3.5 times their regular attack damage plus 2000. To keep it simple, let's assume that everybody's atk is roughly the same. So a full burst would be 5 of such burst attacks. That's 17.5 times regular attack damage plus 10k. 10% of that would be 1.75 regular attacks plus 1k.

An upper end example would be everyone involved being a 3* SSR, with the soul wielding a 3* SSR weapon (but no awakened kamihime in this instance). For the soul, the burst attack's 4.5x + 2500. For the kamihime, it's 5x + 2500 each. Full burst adds up to 24.5x regular attack damage plus 12.5k. 10% of that would be 2.45x regular attacks plus 1,250.