We compare the characteristics of phase-pure MOCVD grown ZB and WZ InAs nanowire transistors in several atmospheres: air, dry pure N2 and O2, and N2 bubbled through liquid H2O and alcohols to identify whether phase-related structural/surface differences affect their response. Both WZ and ZB give poor gate characteristics in dry state. Adsorption of polar species reduces off-current by 2-3 orders of magnitude, increases on-off ratio and significantly reduces sub-threshold slope. The key difference is the greater sensitivity of WZ to low adsorbate level. We attribute this to facet structure and its influence on the separation between conduction electrons and surface adsorption sites. We highlight the important role adsorbed species play in nanowire device characterisation. WZ is commonly thought superior to ZB in InAs nanowire transistors. We show this is an artefact of the moderate humidity found in ambient laboratory conditions: WZ and ZB perform equally poorly in the dry gas limit yet equally well in the wet gas limit. We also highlight the vital role density-lowering disorder has in improving gate characteristics, be it stacking faults in mixed-phase WZ or surface adsorbates in pure-phase nanowires.