How much energy is carried away by neutrinos in matter-antimatter annihilation? Some people say that neutrinos carry away most of the energy, some others say just a fraction. So what is the truth? what is the percentage of energy lost due to neutrinos?
 A: Annihilation of baryon antibaryon proceeds mainly by  a multiplicity  of pions . In this study , table 1, experimental.
Charged pions have a lifetime of of about $10^{-8}$ seconds and will decay into muons and neutrinos (anti too conserving quantum numbers), muons will decay with similar lifetime to electrons (positrons) and corresponding neurinos.
The end stable particles will be neutrinos and electrons to share the charged pions energy.
Neutral pions decay within $10^{-16}$ seconds to two gammas.
Statistically, 2/3 of the energy goes to charged pions, and this is shared  between neutrinos 3/4 and electrons 1/4 (2 $\nu_{\mu}$ and 1 $\nu_e$ and an electron).
Roughly neutrinos will get 1/2 of the available energy.
Gammas take 1/3 of the total energy.
So
A: Anna's answer is good, but it doesn't go far enough.  If you start with equal amounts of matter and antimatter, you end up with equal amounts of electrons and positrons, which eventually annihilate to photons.  You also end up with equal amounts of neutrinos and antineutrinos, which also eventually annihilate to photons.  So those (anti-)neutrinos only keep that energy temporarily. The only other permanent outlet is gravitons, which are entirely negligible.  So eventually,  all the energy ends essentially up as photons.
