Yes! … well, yes and no…
Actually, the cost of living in China depends a lot on you, and on the choices you make. The city you end up teaching in can also play a really large role in the cost of living you experience while in China, but I'll talk about that in a bit.
First, I want to talk about the key choices impacting cost of living in China. For starters, the food you eat and where you eat/buy food are both important factors. To understand how, you need to think of it this way: imagine you are living somewhere in China, maybe a small city, maybe a big city. Now imagine buying Chinese food with Chinese ingredients at a Chinese restaurant with Chinese staff. You won't spend very much money relatively speaking for this meal. Why? Because you're living in China of course! On the other hand, imagine you are living in China, and you buy American style food with American ingredients from an American style restaurant with English speaking staff and menus printed in English. This meal will cost you quite a bit more. Why? Because you're living in China of course! Essentially, the point I want to make here is that if you eat what local people eat, and go where local people go, then the cost of living will be low when compared to any English speaking country. If you decide to eat what foreign people eat, and go where foreign people go, then the cost of your meals will be about the same as in English speaking countries. This goes for grocery shopping as well. Imported cheese from America, butter from Ireland, sausage from Germany, beef from Australia, and milk from New Zealand are all expensive, and buying these on a regular basis will dramatically increase your cost of living.
I don't mean to scary you or put you off coming to China by writing the above, but it's important you know food and products from The West cost extra when you live in The East. Of course, you can go out for burgers, and fries, and pizza, and German beer, and all that good stuff once in a while. So long as you control how often you eat foods from outside of China you'll still save a lot of money every month compared to your home country. I for one have burgers and American milkshakes every Monday at a pretty expensive Western restaurant, but it's ok because the rest of the time I eat Chinese food for all my meals. Striking a balance is key, and you shouldn't be surprised if eating pizza for every meal leaves your bank account hungry for cash.
I just talked about food quite a bit, and that's because food can really make or break your cost of living. Basically, everything else in China is going to be cheaper than in your home country.
Now, with all that out of the way, it's time to talk about cities. The critical point with cities is the more non-Chinese people live in any given city, then the more expensive said city will be. Hong Kong for example is the most expensive city in China. It also has the most non-Chinese people. Shanghai and Beijing are the second and third most expensive cities in China, because they have the second and third highest numbers of non-Chinese people. These cities also have the best burgers, pizza, etc. You'll need to think about balancing how much money you want to save with how much you want to eat like an American, Brit, Canadian, etc. Rent in Hong Kong, Shanghai, and Beijing is far and away more expensive than in other Chinese cities, but EF will pay you enough to have a nice place and still save. For example, I live in Shanghai, and I share a nice 3-bedroom apartment with other EF teachers. Our rent is cheap enough, but the apartment is nice. Now if you live in Chengdu or Wuhan, you can get a 3-bedroom apartment all to yourself for less than the cost of one room in a shared apartment. Here there are tradeoffs, because Chengdu or Wuhan don't have as many cultural amenities in my opinion.
To summarize, you can live in a big city with foreigners and imported goods, but it will cost in rent and the price of food. Or you can live in a small city with fewer foreigners and foreign imports, but you'll spend a lot less on rent and food. It's up to you how you want to make the most of your paycheck through choice you make in food and where you live.