The problem is that Conan was not bringing in the ratings when he took over 'The Tonight Show', whereas Leno was pretty consistent and was beating Letterman a lot of the time. Once Conan took over, Letterman was back on top of the ratings and I'm sure NBC wasn't liking that. They put Leno in the 10PM slot (which was planned prior to his stepping down from 'The Tonight Show' of course) and I think they were hoping that would garner bigger viewers for local news broadcasts and essentially for Conan but as we all see that failed...horribly.
I think in the end Conan was better suited to follow 'The Tonight Show'. He had his niche (so to speak) and just wasn't ever going to go over well with the Tonight show demographic it seems, which is a pity as I think Conan is so very funny.
If he goes to FOX thought I doubt his stint there will last long because he'll just be consistently beat by Letterman and Leno (if Leno stays that is) and FOX is not one to let shows just stay on the air. They are a cancel happy network.