I expect that it is likely the main differences among cryptocurrencies will be the uses to which they are put.
Bitcoin has been looking good as a store of value, but that creates a usefulness for something that is not bitcoin but which is liquid; something that preferably does not tend upwards in value as fast as bitcoin or possibly even tends downwards in value or maybe even has a value that is pretty stable in terms of its exchange rates against various fiat currencies, particularly fiat currencies that are widely used.
The biggest advantage I have seen in this so far has been for financing, since the existence of non-bitcoin cryptocurrencies allows people to use their bitcoin as collateral to secure a loan and take that loan in the form of a different cryptocurrency, one that they expect will not appreciate in value as fast as bitcoin has tended to.
This has let people leave their bitcoins securely locked away in capital accounts, collateral accounts or leverage accounts or however you like to term such accounts while still making use of their buying-power.
Of course it is also useful to have more cryptocoins not just two, because for example if people choose litecoins as their non-bitcoin choice and litecoins start going up in value, they will naturally be wanting to pick yet another type of coin to then serve as their "not going up in value as fast as my collateral does" choice.
The saga of
General Financial Corp illustrates nicely how having a multitude of currencies to choose from can be useful, as well as illustrating how choosing one that does not suit one's purpose can be a problem. (Basically they had to keep shopping around for refinancing because of exchange rates between the currency they were loaning out and the currency in which their own financing was denominated. Though actually in the end they eliminated the currency exchange rate risk by finding financing denominated in the same currency they were loaning out. A currency that appreciates slower would have been better though.)
-MarkM-