Chances are this is a problem with the "master-slave" setting on the optical drives. When connecting more than once device to a single IDE (ribbon) cable, you have to tell the computer which device is the "master" and which is the "slave." This really doesn't make any difference to a typical user, so don't worry about which one should be Master and which should be Slave. However, if they both want to be in the same role, or there's other confusion about roles, than one (or both) will not work.
In order to define the relationship between the two devices, you will need to set their "jumpers." Pictured here in [1]. The jumpers will allow for (approximately) 3 different roles. Master, Slave, or Cable Select (sometimes labeled "CS"). The easiest way to make this work is by setting both drives to Cable Select. This will (usually) make the device on the end of the cable the Master (except when dealing with a 40-pin cable, in which case it might be the Slave on the end). However, it really doesn't matter to you which is the master and which is the slave drive. Just as long as they both know their role and there are no conflicts.
In order to determine how to set the jumpers, look on the drives themselves. There should be a pretty easy to read diagram of how to place the jumpers to achieve certain roles. I suspect that either both of your drives are designated Master devices or that one is Master and one is Cable Select. Either way, that would explain why only one device works.
Hope that helps!
You can get more information from [2].