Question: In age 1, the only resource you buy are the grey ones, because: in age 1, the brown ones produce only one resource at a time, but in age 2 they produce 2. This means you profit more from buying brown cards in age 2 than 1. So it costs a coin, big deal. No matter what, age 1 or 2, when you buy a grey card, it produces one item. This means when the worse cards are in play, you should buy the ones that will be the same.

Note: It also helps to choose your playing style early right?

Answer: 
The analysis is technically correct, but practically kind of wrong.

Every choice of card in 7 Wonders comes with an *opportunity cost*, which is to say, "What are you giving up by choosing this card instead?"

It is true that the brown resource cards in Age 2 give you access to twice as many resources as their Age 1 counterparts, for the cost of a single coin which is usually not huge as far as things go. However, if you decide that this means you should ignore the brown cards in Age 1 and just wait until Age 2 to get them, then:

1. You run the risk of never getting the resources you will need, especially if your opponents are paying attention and carefully deprive you of key cards.
2. You spend less of Age 2 building more useful cards (e.g. Science and Military cards, especially the ones that enable you to build stuff in Age 3).
3. You potentially have to spend more coins building things in Age 1, if you're relying on neighbours to provide the resources.
4. Conversely, your neighbours will not be buying resources from you, denying you a source of income.

It's easy to be flippant and say "It all depends on the cards", but really that's the point - 7 Wonders is a game of making lots of decisions, and there is rarely a singular strategy that you can follow blindly to success.
I think your asking "is it worth buying brown resource cards in age one when they improve in age two whilst grey ones do not"?

The answer is (as it should be for all board games) is "it depends".

yes Age 2 brown cards are better value but you do want to spend a third of the game not getting resources?

Is your choice of what cards you take influenced by what resource yours and neighbours wonder produces.

Do you need to collect lots of the same or a variety of resource for your wonder?

What resources can I get from yellow cards?

So in answer to your question.... Yes age 2 brown cards are better than age 1 brown cards but I personally wouldn't base my strategies on that fact.. However, as in all games, there is never one winning strategy that always works and you should always do what you feel is best in that situation.