The understanding of the charge carrier transport in electronic materials is of crucial interest for the design of efficient devices including especially the restraints that arise from device miniaturization. In this work the performance of organic thin-film and single crystal field-effect transistors with the same active material was studied in detail focusing on the high current density regime, where a pronounced non-hysteretic maximum in the transconductance was found. Interestingly, in this operation mode for both, thin films and single crystals, comparable densities of free and gate-induced charge carriers were estimated. Kelvin probe microscopy was used to measure the contact potential difference and the electrical field along the transistor channel during device operation exhibiting the formation of local space charges in the high current density regime. ; Peer Reviewed ; Postprint (published version)