Sorry for the delay getting to an answer - the holidays have been super busy for me this year.
If you feel up to it, definitely check out the link @ChuckSherrington posted in the comments. That has more information than you'll need for a while.
Getting down to business: The answer to your question is both!
Since your question assumes that both are related and affect each other, I won't go into how they do that.
However, to clear up some misconceptions:
It's not a 1-to-1 cycle.
That is, the "amount" of anxiety reduced by reducing adrenaline is not the same as the amount of adrenaline reduced by reducing anxiety. Similarly, the amount of anxiety created by inducing adrenaline is small compared to the amount of adrenaline created by inducing anxiety.
There are other factors at work
This is where the "parasympathetic" thing comes in. The human nervous system is actually two systems (broken up into the Central Nervous System (CNS) and the Peripheral Nervous System (PNS), though the PNS is often broken down further).
One of the component parts of the PNS is the Autonomic Nervous System. This carries out the largely unconscious functions of daily life: breathing, heartbeat, digestion, etc. It is further split into two components: the Sympathetic Nervous System (SNS) and the Parasympathetic Nervous System (pSNS).
A very rough and reductionist analogy would be to say that these two, together, are like two springs one either side of a ball (or something) - they keep each other regulated and in balance.
The SNS is responsible for very fast, excitatory activity. Fight or flight, for example. The adrenal response is part of the sympathetic nervous system.
The pSNS is a lot slower. One of it's primary functions is to return the body to a relaxed state after it was provoked in an excited state.
From the wiki-books article @ChuckSherrington posted:
While an oversimplification, it is said that the parasympathetic system acts in a reciprocal manner to the effects of the sympathetic nervous system; in fact, in some tissues innervated by both systems, the effects are synergistic.
So as you hopefully have seen, as normal-functioning humans (which, to live, you must have both a SNS and a pSNS; it's not a question), you have a modulation response which keeps the adrenal response (the base response to a threatening stimulus that prepares the body for fast action) from getting out of hand.
Now, lastly, a disclaimer of sorts:
The link between neural activity and thoughts is tenuous at best! Many people are involved in many flame wars over the link between neural activity and phenomenology (experienced reality). The most direct view, and a very common one (from what I can tell) is the view that neural activity is reality itself. That is, our existence, our lives, our individual personalized reality, is neural activity itself.
But you will have to decide that question for yourself, because this is not a philosophy question/answer.
What's important is that the link between having thoughts and having feelings is not well understood. So adrenaline may make you nervous, but it may give Susie Randomgirl a panic attack (believe it or not, I know someone who can work themselves into a panic attack, every time - and they still don't get that they do it to themselves).
