The answer to your question can be quite complicated, since it implies the device physics of the OFET. On the other hand, it was shown that the OFET characteristics can be obtained by the Gradual Channel Approximation, as a standard MOSFET, at least for long channel devices where contact resistance can be neglected. Considering the GCA, the difference in the output characteristics of a MOSFET nd an OFET arises from the non linearity of the OFET transfer characteristics in on-regime, at low Vds. Indeed, since the field effect mobility of the OFET depends on gate voltage, the behaviour of the drain current can be superlinear with Vds You can find more details about the device physics in the paper of Sirringhaus, Adv.MAt.vol.17(2005)p.2411, and about device model in Marinov et al., IEEE trans.onElectronDev. 56(2009)p.2952.
Even though the charge transport mechanism of MOSFET and OFET is totally different, the output curves of ideal MOSFET and ideal OFET should be similar.