I am thinking about buying an expansion. What deck offers more to the game and why? The Reward deck from Incursion or the Hazard deck from Conflict?

More of what, exactly?

The Rewards deck will come into play more frequently, since any winning defensive ally can draw from it.  It adds more Attacks, more Reinforcements, more and different Negotiates, Kickers and Rifts (which are completely new), and a few new Artifacts. It expands what's already there, if you're looking for more of that.

The Hazards deck only comes into play about 3 of every 10 encounters. It changes that encounter in some fashion, be it large or small, and then usually goes away. It is very cool, but very random and fairly unrelated to the other game components.

If you enjoy Cosmic, you will ultimately want both.

Thanks Kobold! For not knowing what I wanted more of you did an excellent job of answering my question. LOL!

Ultimately, I agree that I will have to get both expansions. I was hoping that the hazard deck was more interactive (but from your description is sounds like the reward deck is) because I want the black playing pieces. 

But now you have forced my hand and I will have to buy both at the same time... one for the reward deck and one for the black pieces to match the color of my heart as I play the game. You have to play ruthlessly in this game.

Thanks again!

I always play orange, so Cosmic Incursion would have been the must-buy for me based on that!  But the black ones are really nice, and very popular with everyone else I play with.

Thankfully, neither expansion is terribly expensive!

 I definitely agree that both are must-buys.  But if I had to get one for the deck, I'd go with Rewards.  Hazards are neat but come into play less often, generally, and Rewards makes it easier to play with a bigger group of players, especially when you have lots of card-drawing powers.  

But if I were to get one for the aliens, I'd get the newest one.  So basically, you have to get both!

My only reservation about the Rewards deck is the vague conditions that cause Rifts to explode.  We've debated that quite a bit on BGG, and come up with a consensus, but boy does that ever need an FAQ.  (Consensus: they only blow one when someone involuntary takes one away from you; you can't give someone a Rift voluntarily and expect it to explode.)