Restaurants can generally be categorized based on the type of furniture they use. It is highly unusual to come across a restaurant that is trying to give an air of traditional dining when their restaurant chairs design is based on metal.
Wood of course can work in either modern or traditional restaurants. Metal is more suited to the modern look in restaurants - in fact it is that modern look that makes them appear out of place in traditional restaurants. Of course, I wouldn’t rule metal out completely - there are some very traditional looking chairs around based on metal frames.
Metal framed chairs that have been painted a dark color together with very traditional looking backs and seats can work reasonably well. Metal chairs that are polished and show their natural silver look are a different matter - they often don’t fit the decor.
Unfortunately, metal frames are becoming the norm now, even for popular finishes such as teak, bamboo or leather. Rattan chairs built on aluminum frames look great, but oh so modern. There is no way you could hide them in an old traditional style restaurant.
Before deciding on your restaurant chairs design, settle on a theme or style for your restaurant. Then look for restaurant chairs that will fit in well with your restaurant. Whether its metal or wood, there will always be a restaurant chairs design to suit your restaurant.