I am under the impression that face is EVERYTHING to EVERYONE. Rich, poor, north , south , east , west ........

I believe they rank as follows:

Face
Money
Family

Compassion is for the rich (they're the only ones who can afford it, not my logic but an attitude I've heard expressed by many people)

Mankind ? Psh .

And love goes right beside money , cuz they LOVE MONEY

"Face" in China is like the game maybe you used to play (I did) when you were a child. My father is policeman, then the other kid, to show his father is stronger, would say my father is pilot, the next one would say he is a doctor.....

However, if for children it's just a game, in China, this "childish" behavior is sometimes really up to the extreme and taken very seriously. For instance, Chinese people won't mind laughing at a foreign president making a mistake, but they wouldn't do it with their president who will then lose his face to the public.

As for your question, what's more important, I will stereotypically list the Chinese way as I imagine it goes :
At first money, face comes second if by losing it you get more money (it's more or less like the kissing asses we have in western countries), then family (providing that by family, you also includes in-laws, uncles, aunts, etc, not just you, your wife and your kid and that you bring all these joyfuly people wealth and gifts), then love, compassion (for what they see on TV only, not in the real life) and eventually mankind (providing that Chinese knows that people with not such an extended 7000 years old culture and traditions are worth their interest).

I really don't understand "face"....

If you think you are important and should have face how does throwing an outrageous tantrum help?

I am reminded of that "Bigwig" at Kunming Airport who trashed the boarding gate because he was late and missed the call.

How is this kind of behaviour supposed to keep face?

Western ppl look at this and think "Bloody child!...grow up!"

How do Chinese ppl see this sort of behaviour?

Is it a case of "Oh...he must be important because he is behaving like an utter t*sser, only really important ppl can do that"

I really don't get it....

The Chinese obsession with face saving is a far stronger and more irrational than in other countries. But not all Chinese are obsessed with face. It's usually only the less intelligent long nails farmer types. 

I don't think any country or people are free of it. I would argue that the individuals who come on this forum and always make a point of going "I'm successful I have a nice car, nice house I'm not a lowly teacher are engaged in far cruder obsession with face than the farmers

I was surprised last week a lot, how much face is important.

 I got a customer, who is buying some product from us. we are buying it from factory.

we need to specify exact software version and accessories for given product. So have our customer.

Our client  got request from his client, which got it from his client. complicated a bit. big chain with many hungry fishes. Anyway, it is that simple. We have provide the list of accessories and software versions for that product. something u can use only with higher version. they have tried to go with the cheapest version with full accessories set.

We provided price, but excluded one thing. everyone did not seen that, include me. so they got contract, but when they come sign with me, we find out this part is missing from pricelist. then start the process of talks with supplier and customer. it lasted 10 days here, to ask end user if he really wish to use all things so we offered discount for full version, or go with original version requested, but without that part.

 So during this 10 days, my client did n ot talk with no one, but me, just because he was afraid to lose face and look not professional to his clients. so he made the decision himself. delayed the contract and possible delivery, while all the time he was counting, if the profit he have from cheaper version would cover the high version and how much it will keep in pocket than. But no way to tell end user what is going on and what is his wish. because he would need to tell him ,that we made mistake...

I was wondering the other day about that. I saw a group of Chinese guys at a restaurant and they'd bought a bottle of wine. 

The service there was fairly terrible and the waitress just dumped the bottle on the table with a corkscrew and walked off. So I was watching them try and open the bottle and they couldn't do it, as they've obviously not used that kind of corkscrew before so I went over and asked if they would like help. 

They said yes and I showed them how to do it, then they all clapped (it was actually quite embarassing)

But I went back to the table and my friend told me that I shouldn't have done that because now they've lost face because a young-(ish) girl helped them with something. 

I thought I was helping them save face as they were really struggling with the bottle. 

hmmm