Residual astigmatism is common after cataract surgery involving implantation of an intraocular lens, yet the tolerance of presbyopia-correcting intraocular lens to astigmatism of different magnitudes and axes is poorly understood. Here we compared visual acuity and quality in the presence of induced astigmatism after implantation of a trifocal or extended-depth-of-focus (EDOF) intraocular lens, the two widely used presbyopia-correcting intraocular lenses. At least 3 months after implantation of a TFNT00 or ZXR00 intraocular lens, patients were analyzed by slit-lamp examination, non-contact tonometry, subjective refraction, iTrace aberrometry, and corneal topography. After correction of residual astigmatism, astigmatism of different magnitudes on different axes was induced using cylindrical lenses, and overall visual acuity was measured, while objective visual quality was measured using the Optical Quality Analysis System II. Subjects were also asked about subjective visual quality using the Visual Function-14 questionnaire. Comparison of 18 individuals who received a trifocal lens and 19 who received an EDOF lens showed that objective visual quality was better in the EDOF group regardless of the magnitude or axis of the induced astigmatism. In both groups, astigmatism of at least -1.00 DC influenced distant vision more severely when the axis was 45° than 0° or 90°, meanwhile astigmatism of at least -1.50 DC influenced near and intermediate vision more severely when the axis was 45° than 0° or 90°. Trifocal or EDOF intraocular lenses are less tolerant of oblique astigmatism than astigmatism with or against the rule. EDOF lenses may provide better objective visual quality than trifocal lenses in the presence of astigmatism, regardless of its magnitude or axis.