This has more or less nothing to do with testosterone. You can lift more weight when you feel like you're in "danger" because of adrenaline. Basically, when you do weight training, your body and CNS only let you exert a certain percentage of your total muscular contractions. This is because your body is trying to make sure you don't get injured by applying more force than you can actually handle. When you have an adrenaline spike, your body lets you increase this percentage that I mentioned above, and therefore you can use more of your total strength. This has nothing to do with testosterone. For example, I'm sure you've heard of mothers lifting/pushing cars in order to save their babies etc...
Now to answer your actual question, if we are talking professional level of bodybuilding and fighting, then it is bodybuilding WITHOUT QUESTION. At the pro level of bodybuilding, you can be sure that at least 90% of the athletes are supplementing with anabolic steroids, which are just derivatives of the testosterone compound. For example, on average a young male will produce somewhere around 6mg of testosterone per day. Now, a bodybuilder trying to turn pro, or already pro, will supplement with MINIMUM 500mg of testosterone a week!
Now, if the bodybuilder is natural, then it could go either way. The amount of testosterone that an individual has will largely be impacted by genetics and their lifestyle. What I mean by lifestyle is largely composed of their diet and sleep. The training won't have much effect, given that both of them are doing some form of strength and high intensity training. Keep in mind however, that the fatter a person is, means the more estrogen they will have (opposite of testosterone basically).
I hope that answers more or less all your concerns.