It's not actually confirmations that are important, but the amount of work that has been done on top of a block. With this in mind, coins that have a target time that is different than Bitcoin's (10 minutes) will have a different amount of work going into a single block. For example, if the target time for a coin is 1/4 of what Bitcoin uses, than you'd need 4 times as many blocks to consider it just as safe.

There are also other factors that go into how safe a block is from being orphaned after it is initially accepted, but they mostly have to do with mining centralization and the availability of mining power that is not currently on the network. The main factor is the target time.