There are many factors one might consider in making this decision. I'm going to group them into three areas: Film, Abstraction, and Time and Timelessness. There are almost certainly others, but I think this hits the highlights.
You might be shooting with film in the 21st century.
Every different film stock has different character, and you might like that particular character. Going into the details of available films is a whole big article of its own — and frankly, beyond my expertise — so I'll just leave this as a point to consider without further expansion.
Or, you might be developing and home, and it's much easier to do black and white at home than color. (In fact, the conclusion to How do I develop color negative (C41) film at home? is effectively "it's not economically feasible".) So, of course, that would make the decision easy.
You may also be interested in a particular paper or print process — these two each have their own characteristics. Maybe you want to make platinum-palladium prints, which have a distinctive warm look and a very large range from dark to light.
But, if you're shooting digital, or if the above otherwise isn't a big factor, there's....
All photography inherently includes some amount of abstraction. A three-dimensional scene is rendered flat, and a moment is extracted from the flow and movement of time. Black and white is another level, cutting away what is normally an important part of our visual perception.
In particular, black and white tends to emphasize forms and contrast — the shape of something can easily become more important than what it is. The same can be said of simple, bright (and usually human-created) color, but black and white really pares things down. With human subjects taken to the extreme, this can become bodyscape photography — not normally the head/face/neck photographs you're interested in, but you might consider if you want to make some images where shape is more important than subject per se — or at least emphasized.
At the very least, this abstraction can simply be used to de-emphasize a distractingly colorful background. For formal or semi-formal portraits, it's ideal consider that before the shot is taken, and hopefully arrange the situation better, but... sometimes not possible, or sometimes, too late. In any case, this can do the opposite of the above: emphasize your subject with less care for the surroundings.
This can be used as a crutch, too — perhaps the white balance is messed up due to mixed lighting, and simply removing color hides the problem. It's often the case that highly overexposed or highly underexposed images pushed into an acceptable range seem better in black and white, both because artifacts (chroma noise, discolored highlights) are hidden and because viewers are more likely to expect a black and white image to be an intentional graphic composition.
Or, we can look at this the other way around: what does color add to a portrait? In particular as it relates to people and portraits: skin, eyes, clothing. Does your subject have striking eyes which contrast with or are complemented by clothing, background, accessories? Without color, you'll need to carefully consider the shape and position of the eyes and other features, and rely on shape and contrast to direct the viewer's focus.
Do you want to show the rich hues of their skin, or color of their lips? In color, it's important to get things just so — even over the vast range of human tones, these are strong memory colors, and small changes can look unlike your subject — or even into the uncanny valley and not properly human at all.
Going to black and white gives you freedom from this. You have a wide latitude to adjust from low-key to high-key, depending on the mood and look you want to convey. This also lets you adjust the relative strength of different color channels — the digital equivalent of shooting in black and white with a color filter. (In fact, see: Which color filter do I use for a black & white portrait?). This opens up a range of possibilities not open to color photography. For example, red or orange filters can mask skin blemishes — although they also tend to vanish lips (so you may want blue makeup to compensate).
Time and Timelessness
Photography is unique as a visual art because it is so tied to modern technology. Color film wasn't commercially viable until the mid 20th century, and wasn't really the choice of the masses until the 1980s. So, going black and white is a cheap way to harken back and make a photograph seem old timey.
That sounds kind of lame — and, I think it often is... an easy "instagram filter" choice with no real consideration. But, it can be more than that, too. Color anchors us in time in more ways than just tech progress — think avocado green and harvest gold from the 1970s, neons and black from the 1980s, blues and earth tones from the 1990s... color is fashion, and fashion is fickle. Going to black and white frees us from that.
Additionally, many great portrait photographers over the years have worked with black and white, either by choice or because of the time they were working. If you want to emulate their look and style (and, imitation is not just flattery, but also a strong learning technique!), black and white is simply given... although, it strikes me as a good exercise to try to reproduce the feel of a black and white portrait you like in color instead. (What works? What's different? Is it vital?)