Objective: Evaluate and compare the image quality and acceptance of a full MBIR algorithm to that of an earlier full IR hybrid algorithm and filtered back projection (FBP). Methods: Acquisitions were performed with a 320 detector-row CT scanner with seven different dose levels. Images were reconstructed with three algorithms: FBP, full hybrid iterative reconstruction (HIR), and a full model-based iterative reconstruction algorithm (full MBIR). The sensitometry, spatial resolution, image texture, and low-contrast detectability of these algorithms were compared. Subjective analysis of low-contrast detectability was performed. Ten radiologists answered a questionnaire on image quality and confidence in full MBIR images in clinical practice. Results: The contrast-to-noise ratio of full MBIR was significantly higher than in the other algorithms (p < 0.0015). The spatial resolution was also higher with full MBIR at high frequencies (> 0.3 lp/mm). Full MBIR at low dose levels led to better low-contrast detectability and more inserts being identified with a higher confidence (p < 0.0001). Full MBIR was associated with a change in image texture compared to HIR and FBP. Eighty percent of radiologists judged general appearance and texture of full MBIR images worse than HIR. Moreover, compared with HIR, for 50% of radiologists, the diagnostic confidence on full MBIR images was worse. Questionnaire reliability was considered acceptable (Cronbach alpha 0.7). Conclusion: Compared to conventional iterative reconstruction algorithms, full MBMIR presented a higher image quality and low-contrast detectability and a worse acceptance among radiologists. Key points: • Full MBIR used led to an overall improvement in image quality compared with FBP and HIR. • Full MBIR leads to image texture change which reduces the confidence in these images among radiologists. • Awareness of the image texture change and improved quality of full MBIR reconstructed images could improve the acceptance of this technique in clinical practice.