I would actually argue it is very fundamentally different. Once you've dug up your chucks of metal, trading them with others requires very little extra energy to be expended (Especially if we're going to go all the way to talking about actual cash, which is easy to split-up into smaller denominations).
Vs. Bitcoin, which will still require miners to expend the same amount of CPU cycles to keep the network working so you can transfer your Bitcoins to others, even after all of the Bitcoins are mined and the blocks provide no new Bitcoins into the market.
It'd be interesting to see a table of 5 year energy cost from inception of a bar of gold vs. equivalent value of Bitcoin, at various #s of transactions.
Vs. Bitcoin, which will still require miners to expend the same amount of CPU cycles to keep the network working so you can transfer your Bitcoins to others, even after all of the Bitcoins are mined and the blocks provide no new Bitcoins into the market.