How visible the nostrils are, depends on these factors:

Head posture

Obviously, if the model tilts the head back ever so slightly, more nostril will be visible. If the head is slightly tilted down, you see less.

However, there are some effects even if you shoot the photo dead-on:

View plane of the Camera

Especially in your example image, you can see that while in both cases the camera points directly to the face, the height of the camera is different.

In image one, the camera in on the height of the tip of the nose, maybe even the upper lip. This perspective allows to view more of the nose from below.

Image two has the camera on eye level. This means we are now more looking down on the nose from above, so that we are seeing less nostrils.

Focus Length

And second the focal length of the lens used. The focal length translates to the angle of view, which changes the look of an image drastically.

A short focal length or wide-angle lens over-pronounces the size of closer objects or features to the lens. This can make a nose to look more prominent, as it is closer to the lens. The effect is getting even more prominent, the closer the subject is to the lens (with a wide angle lens, you need to be much closer to the subject for filling the frame with it).

You will notice:

• Noses pointing towards the camera will look like sticking out
• Oval head shapes will tend to look more oval
• Ears seem to appear to be flatter on the head
• The changes of the camera level will be more apparent due to the wider view angle. If you are lower, then the wider angle will make the nostrils even more visible. If you are higher, even less nostrils will be visible.

A longer focal or telephoto lens on the other hand under-pronounces sticking out feature, so that faces tend to look flatter.

Effect:

• Faces will look flatter with noses not sticking out
• Heads will look a bit rounder
• Ears will appear more like the are. There is no artificial "wrapping around" effect.

Note that the focal length shown here are on a full frame camera.

So why would anyone use a wide angle lens in portraiture?

There can be several reasons.

• A wide angle lens can help cover some feature, like sticking out ears.
• It allows you to get very close to the model, and this can create a feeling on intimacy.
• It allows you to capture more of the surrounding of the model, which is useful if that context is needed for the photo's message.
• At a lot of people are used to the look due to their mobile phone cameras also being on the wide-angle side, so they might find their image looking more familiar.
• It can create a photo that looks more dynamic by using the skewing effect to emphasize e.g. movement.

Summed up

• The top image seems to use a longer focal length and is shot on a lower view plane, which makes the face rounder, the nose sticking out less but also gives a view of the nostrils
• The second image is shot a bit wider, making the head more oval, the nose a bit more prominent, but also due to the higher view plane helps to hide the nostrils.