You will technically have double the coins. But since a hard-fork will support the same functionality as the other, it's highly possible that the value could split.
The point to note is whether the combined market cap after the split is more than the market cap of Bitcoin pre-split. If that is the case, the split has in fact created value.
Bitcoin rely a lot on its network effect, which means it is the most known/accepted token, because it was the first one. If it splits and both chains go on, the network effect may be broken nearly by half, which would weaken bitcoin as a whole.
One of the reasons advanced by Roger Ver for the split is that Ethereum as a whole (ETH + ETC) has risen in value after the hard fork.
So not all forks result in destruction of value.