Apply a reference signal at the input with known spectral content and then measure the spectrum of the signal at the output.
You might need to build a test-harness to do this that interposes a signal at the output of the VOIP codec, and captures the output of the audio graph to a file.
I personally doubt that the iPodEQ is doing anything other than EQ, so I would expect the two outputs to be identical. Again, this is easily verified.
In terms of input signals, I would recommend either Pink or White noise.
There are plenty of tools with which to view the spectrum of your recorded signal. If you haven't got anything to hand already, I'd go for Sonic Visualiser if you've not got something to hand already. On the spectrogram it will be quite apparent if the correct EQ curve has been applied.