The first stage is meant to be more relaxing, while the second stage is invigorating, and promotes awareness.
If you haven’t managed to develop enough relaxation, then the second stage can feel a little stiff and awkward at first. The problem is probably that you’re exercising some kind of subtle control over your breath. Breathing is one of these things that’s best done automatically.
In the first stage of the practice we’re just acknowledging the sensation, because we count after the out-breath. So there’s less possibility of trying to control the breath — you can’t control what’s in the past. But in the second stage there is a sense of anticipation — and it is possible to control what’s about to happen. When your desire to control events meets a sense of anticipation, then you find yourself taking charge of the breathing, rather than just watching it.
Since your unconscious is much better at regulating your breathing than your conscious mind is, you find that your breathing is a bit stiff.
This problem will sort itself out soon. You’ll find that you relax into the second stage if you just patiently keep working at it. At some point you’ll get a bit more concentrated and “forget” to control your breath.
However, if you need to, you can always drop back into the first stage of the practice, and return to the second stage when you’re more relaxed. Or you can consciously work in the second stage to develop more relaxation by really letting go on the out-breath.