If you answered gold you need to go think again.
If you answered they weigh the same you also need to think again.
The answer is that the feathers weigh more than the gold. And the fault that this is the answer lies with the United States of America.
Huh???? you cry out!
As you would know the entire world officially uses the metric system except for Myanmar, Liberia and the United States. England is mostly there - but not quite.
If the imperial system was banished into the past by all countries then the "ton" referred to above would be a metric ton (or tonne) and be 1000kg. i.e. feathers and gold would weigh the same.
However because the USA refuses to go, it turns out the world still measures precious metals using the ounce. The Troy ounce in particular.
And yes folks this is why the imperial system needs to be removed from this world, because in the imperial system there are many different types of ounce. A Troy ounce (480 grains) and an avoirdupois ounce (437.5 grains) are the ones in use today in the US. And to make things even more fun, there are 12 oz to the Troy pound and 16 for the avoirdupois pound. Go figure.
So the US insists on sticking to this bizarre system and because of this the rest of the world has to suffer the fact that precious metals are all measured in Troy ounces - throughout the world.
So back to our puzzle. By "ton" what did I mean? Well with gold it has to be the Troy ton. But hang on, more imperial confusion now follows...
We have the short ton and long ton. Which is it?
If we are answering this problem in the US, then we'd use the short ton which is 2000 pounds for both feathers and gold. If we are in Liberia then we'd be using the long ton 2240 pounds. If we are in Australia then the ton of feathers is metric and the gold is a long ton. In all cases the gold is measured in the Troy system.
To actually answer this probem we're going to need to do some conversions. The easiest method is to convert all weights to metric and then compare.
Now a troy ounce is defined as 31.1034768 grams. (Yes that's right it is defined using the metric system. In fact all imperial measurements are defined in metric and have been for nearly a century in many cases.) So with 12 ounces to the Troy pound we have a short ton being 746.483 kg and the long ton being 836.061 kg.
Our avoirdupois ounce is defined as 28.3495231 grams. So therefore with 16 ounces to the pound and either 2000 or 2240 pounds to the ton we have a short ton being 907.184 kg and our long ton being 1016.047 kg.
And finally we have our lovely metric ton (or tonne) being 1000kg.
Looking at the figures you will see that in all combinations of short, long or metric that the Troy ton is smaller than all others.
So no matter which country you are in the ton of gold weighs less than a ton of feathers.
Now when the US finally goes metric, which it eventually will (if not to save the economy billions of dollars but to also save the lives of the thousands of people dying each year because of incorrect dosages caused by incorrect conversions) then the original question as posed would be answered correctly as "they weigh the same". Until then the world is stuck with this abortion of a measuring system. Stuck back in the dark ages.
P.S. If you're still not convinced, watch this: http://www.youtube.com/watch?v=Omh8Ito-05M for a laugh. If the guy had a metric ruler he would have read 140mm and 180mm and worked out the difference in no time.