In Cantonese, you usually use 面 to mean
However, it seems like in Mandarin, people use 臉 (e.g., 我的臉很紅) sometimes and other times use 面 (e.g., 面對面).
What are the guidelines around using 面 or 臉?
In modern Chinese, when it comes to the meaning of "face, they basically are the same. However, in classic Chinese, they mean differently. Knowing the origin of them may help you understand how they are used in words.
面 meant "face"; however, 脸 is used to refer to face now.
脸 meant "cheek"; however, 脸颊 is used to refer to refer to cheek now.
Below is an abridge of a Ci poem written by 晏殊 in Song dynasty
It's the case that (she) won the game of 斗草 this morning, (so) smiles come out of her two cheeks.
As you can see, a man can not have two "faces". Since southern dialects remain more classic Chinese elements, you can find 面 more when it comes to face. As far as I know, in shanghai dialect, 面 is also used that way.
So a rough guideline is:
in literary and archaic words (for example, idioms), 面 is used more; while in colloquial words, 脸 is used more.
For example, there is a word 面目 (meaing: appearance,looking). However, you would say 脸和眼睛 when you refer to "face and eye". Regarding your example of "面对面", you can actually say "脸对脸". However, they are different. you can say：
In case 1,"面对面" actually means "physically close" (e.g., not on the phone). Your face is not neccessarily opposite his face. While in case 2, "脸对脸" means "facing each other", so their faces are opposite. If you use "脸对脸" in case 1, it sounds very strange. If you use "面对面" in case 2, it sounds too formal.
面 could mean:
surface; top: 路面，地面，平面
side; aspect: 方面
extent; scope: 知识面
flour； powder: 白面, 胡椒面
脸 could mean:
face; facial expressions: 笑脸，圆脸
feelings & sensibilities: 脸面
Both 脸 and 面 could express feelings & sensibilities: 面子，不给面子， 脸面，给脸不要脸， 不长脸。
There is also a phrase 脸皮厚 or 厚脸皮, meaning thick-skinned or have a audacity to do something.
That's pretty what I can think of.
rule of thumb. when you see a character with '月' component that describes a body part, it usually refers to the organ.
so in your case, '脸' refers to face as a person's body part, while '面' refers to the person him/herself in a social situation.
take '面对面' vs '脸对脸' as example. '面对面' can be translated to 'face to face' or 'in person' as the two parties are physically close to each other, while '脸对脸' can only be translated to 'face to face' and emphasizes the fact that two faces are facing to each other.
Basically they can mean the same meaning. But there are phrase where only one of them works. They are more or less a kind of custom and no specific rules.
There is even a phrase
脸面, but you can never say
However, generally speaking, 面 is a more literal/abstract/elegant form than 脸, and 面 can mean more than just face, e.g., 对面(the other side), 全面(total).
面:Used in written language. 脸:use in spoken language. Face: 1. The face of the person, the front of the head. 2. The adjective refers to a person's dignity and face. 3. Relative to face, such as: back mountain water. 4. In person, direct contact. 5. The shape of the line movement of geometry. 6. Aspects, such as: fear of all aspects. 7. Quantifiers, such as: a mirror. 8. Flour made from grain. 9, the food fiber is small and soft. Face: 1. The person's face, the front of the head, from the forehead to the chin. 2. The front of the object, such as the face. 3. The adjective refers to a person's dignity and face.