The recent CLAS 2005, SAPHIR 2003, LEPS, and the old, pre-1972, data on K+Λ photoproduction are compared with theoretical calculations in the energy region of Eγlab<2.6 GeV in order to learn about their mutual consistency. The isobaric models Kaon-Maid and Saclay-Lyon, along with new fits to the CLAS data, are utilized in this analysis. The SAPHIR 2003 data are shown to be coherently shifted down with respect to the CLAS, LEPS, and pre-1972 data, especially at forward kaon angles. The CLAS, LEPS, and pre-1972 data in the forward hemisphere can be described satisfactorily by using the isobaric model without hadronic form factors. The inclusion of the hadronic form factors yields a strong suppression of the cross sections at small kaon angles and c.m. energies larger than 1.9 GeV, which is not observed in the existing experimental data. We demonstrate that the discrepancy between the CLAS and SAPHIR data has a significant impact on the predicted values of the mass and width of the "missing resonance" D13(1895) in the Kaon-Maid model.