It just clicked in my head.

Respawn, who is headed by the ex-CoD guys, is working for EA to make a futuristic sci-fi shooter. This is being made to compete directly with titles such as Halo, Gears, and... Bungie's new sci-fi shooter title code named "Destiny." Bungie happens to be making this "Destiny" project under Activision.

So, with these two headstrong developers making new entrants into the sci-fi shooter world, who will come out on top?

Never bet against Activision. 

The Halo series has never really appealed to me, and I loved Cod4 and I think Infinity ward have some epic potential outside of Activision.

But objectively speaking, Bungie have much more experience building great sci-fi shooters

For this to be a comprehensive fight you must include Halo in the mix as well as that will surely be competing with these other two titles. If you're wondering about just these two titles... It's a really tough call, but I think I may have to give it to Bungie. Activision is superb at marketing, more so than EA I would think, and I believe that 'From the creators of Halo' will hold more weight than 'From the creators of Modern Warfare' in this instance.

this one is gonna be won by Respawn

I have to root for my boy, Bungie.

I included these two developers only since they're both working on *new* sci-fi shooters. Halo as a property has already proven itself and so I didn't include it here.

I'm more interested in how these two companies bring up their new sci-fi ideas, and which one will trump the other.

It also makes it more fun because both developers have an amazing developing background and are working for the two huge rival companies: EA and Activision.

I'm going to say Bungie. Proven company as to Respawn could completely flop

Bungie is an established studio which created great titles such as Halo.
Respawn is a noob studio.

Bungie is backed by Activisions huge marketing machine.
Respawn is backed by EA.

Bungie's game would have to receive extremely poor reviews for it to flop.