EventEmitter - You expect to intermittently get individually completed values that you do whatever with and then discard. These values may be grouped into useful sets by the EventEmitter (each separate event type).
Streams - You expect to get raw partial data that you want to do your own buffering and handling with. You want to be able to feed this raw data to a different target (e.g. file writing) without handling the fine details yourself.
Promise - You expect to get a single completed value when an action is completely finished, or (for a Promise without a return value) you just want to have something contingent on an action finishing.
An example of each:
Streams: A TelnetConnection class that handles connecting to a server, then supplies a stream with the bytes from the connection (with each chunk being whatever is convenient for buffering purposes), and ends the stream when the connection drops.
EventEmitter: A TelnetHandler class that uses TelnetConnection and fires an event for each complete line (ending with \n).
Promise: A TelnetHttp class that has a method get(hostname) that uses TelnetHandler and returns a Promise for the full text return value of doing a simple HTTP GET call.
Thanks again for the help!