Both have an infectious, primitively organic, swarming/insectoid race that spreads across planets (and between planets) leaving a wake of destruction.
Both have an advanced, psionic, religious, robitically enhanced race whose goal is to eradicate the infectious race, and do so by using their advanced technology to destroy entire planets that have been infected.
Both have humans, who naively enter the conflict through recent innovations in space travel, and become very concerned with the fact that they saw the advanced race destroying planets, not understanding what it is for. Humans get aggressive against the advanced race and this makes the advanced race feel like humans might get in the way of their holy conquest of zerg/flood eradication, causing them to become fully hostile back at humans.
Also, both have hints towards a great ancient space race who created everything, and who the advanced race worship as gods and use the technology of. Additionally, the infectious race turns against this ancient race in both. In starcraft its obviously the Xel'naga, and in halo it is the forerunners, who also created the halos.
I literally keep thinking of more and more things that are almost if not exactly the same.
I'm not saying its a bad thing, I like the complexity of the relationship, and I am a fan of the stories and gameplay of both games. I just thought it was pretty neat that the relationships are basically exactly the same.
Flood = Zerg
Covenant = Protoss
Humans = Humans
Xel'naga = Forerunners
And each literally has only those races, no more.