Well off, better off
Mariano from Spain writes:
  How do I understand the sentence: We are better off than you.? Does it always refer to questions related to money? For instance: We have got more money than you. I don't think so.
Roger Woodham replies:
Well-off relates mainly to money matters. If you are well-off, you may not be rich exactly, but you have enough money to live well and comfortably:
By central European standards they are quite well-off They have their own flat and drive new cars.
well-off for
However, if you say you are well-off for something, this means that there are many of them:
We’re well-off for coffee shops in this town. There's one at every corner in the High Street.
The comparative form of this adjective is better-off which is used to talk about the varying degrees of wealth different people have:
We’re not as well-off as the Jones's. They’re definitely better-off than we are. Just look at the way they dress!
To be better-off, as you suggest, Mariano, also has another meaning of being in a better situation and is used mainly in conditional patterns as follows:
If you've got heavy bags to carry, you’d be better-off taking a taxi.

It says on the sign that the motorway ahead is blocked. You’ll be better-off if you leave the motorway at this junction which is coming up now.
the better-off
The better-off is sometimes used as a noun to describe a category of people, cf the rich / the poor:
The rich and the poor live side-by-side in this part of town.

The better-off should pay a higher rate of income tax, while those who are worst-off should pay no tax at all.