Vega's really competitive and used to thinking in terms of everyone ever being a potential rival. Giant robot fightan gaemz are the favored spectator sport of his planet and he's a prodigy, so it's second nature.

I have probably as much if not more headcanon for the Fury than I do for Vega. :P It's unusual for a Zoid in that it's reasonably intelligent/fully sentient/capable of learning. It also shows very marked aggression and competitiveness. It's prone to getting so overcome with rage that it is uncontrollable and just rampages regardless of what it's being told to do. That's all canon there, but it gives no real reason for why that is. The Berserk Fury's ancient, having been discovered in a dig site, so my theory is that it lost its pilot long ago and has basically been driven mad by its grief. All it really has left is the ability to FIGHT AND DESTROY THINGS, so it clings to that with all it has and only accepts very gifted pilots (in this case, Vega) so that it can fight at its fullest potential.
I think that the Fury is, on some level, just looking for a way to die/be put out of its misery. The thing is, it has yet to find anything that can successfully do the job (though the Ohm came close) and it will not give an inch in a fight. (In the case of the Ohm, Stacy had to call the Fury off herself after part of its armor was melted off and Vega was knocked out.)