The differences would be the impedance of the output and balanced vs unbalanced signals. The main outs are 440 ohms balanced and the headphone outs are 55 ohms unbalanced.

In general, when running a headphone out into a line in it should sound fine but the level might be slightly lower than the same signal coming out of the line outs (as far as I know) and you might run into more distortion and noise. Balanced cables also are less prone to distortion, especially over longer cable lengths, which you lose with the headphone out since it’s unbalanced The individual outs on the Rytm are also unbalanced and that’s not a big deal really. The outputs on Elektron gear seem to be very high quality and you shouldn’t have any issues. You could always run a couple of main vs headphone tests and look at a spectrograph to see if there’s any added noise but it should work ok.