I forgot to report : I started a new campaign, and after 3 game months of playing, I have one standing critic : there seems to very little incentive to actually capture live or dead aliens or cultists "as soon as possible". If you heroically recover a corpse or live specimen and abort out of a hopeless situation, it's actually not useful, because the captured stuff will stay in the research queue for months. It's especially disappointing that if you delay lifesaving items (van, bulletproof vest, magnum) for a month to research alien stuff, nothing gets unlocked. There may be bonus score (and thus more money for the next months), but then it would be better to show the score in the ufopedia screen itself - and for non-humans, it had better be a 3-digit number.
About practical gains, I don't know, but if XCOM manages to prove an alien threat by bringing back corpses/specimen, this could unlock random pieces of "military-grade" items (grenades, smoke), as they are bringing proof that they are facing something big.