For the first time, the predictive capabilities of the mixed Bohm/GyroBohm,Weiland and 'retuned' GLF23 transport models are investigated with discharges from the ITPA ITB database by fully predictive transport simulations. A range of plasma conditions is examined for JET, JT-60U and DIII-D discharges with ITBs. Fully predictive transport simulations show that the predictions with the Bohm/GyroBohm model agree very well with experimental results from JET and JT-60U. This indicates the importance of the interplay between the magnetic shear and ωExB flow shear in ITB formation. In order to achieve a good agreement in DIII-D, the -stabilisation had to be included into the model, showing the significant role played by the a-stabilisation in governing the physics of the ITBs. The Weiland and GLF23 transport models show only limited agreement between the model predictions and experimental results. The Weiland model fails to form a clear ITB in any of the three tokamaks, the main reason being the oversize growth rates of ITG and TEM. The growth rates exceed significantly the wExB shearing rates and the growth rates calculated with the gyrokinetic code kinezero. The average temperatures and density predicted by the Weiland model are typically in fair agreement with experiments. The GLF23 model often predicts the ITB, but its radial location is too far inside the plasma. This leads to strongly underestimated central temperatures. The heat transport outside the ITB is very well reproduced by the GLF23 transport model. The discharges modelled here are the same as studied with the gyrokinetic flux tube code kinezero by C. Bourdelle et al. in this journal.