Looking at the studies, using a water flosser in combination with a manual toothbrush is more effective than using string floss (Goyal, et al. 2013).
It seems however, that there have been no studies on comparisons between water flossers and air flossers since Sarma, et al. (2012) which you posted in your question, which states
The use of the Waterpik Water Flosser removes significantly more plaque from tooth surfaces (whole mouth, marginal, approximal, facial, and lingual) than the Sonicare Air Floss when used with a manual toothbrush.
On top of that, the ADA Council On Scientific Affairs awarded the ADA Seal of Acceptance to five Waterpik Water Flosser product lines based on its finding that they are safe and have shown efficacy for removing plaque along the gumline and between teeth and for helping to prevent and reduce gingivitis (ADA, 2017).
“This product was shown to reduce plaque and gingivitis in areas between the teeth, often the most difficult areas for patients to effectively clean,” said Dr. John Dmytryk, chair of the ADA Council on Scientific Affairs’ Seal Subcommittee. “By granting the ADA Seal of Acceptance to the Waterpik Water Flosser, consumers for whom these devices are appropriate can be confident that they can be a safe and effective component of their daily oral care when used as directed.”
ADA (2017). ADA News: Waterpik Water Flosser first in its class to earn ADA Seal Retrieved from: https://www.ada.org/en/publications/ada-news/2017-archive/february/waterpik-water-flosser-first-in-its-class-to-earn-ada-seal
Goyal, C. R., Lyle, D. M., Qaqish, J. G., & Schuller, R. (2013). Evaluation of the plaque removal efficacy of a water flosser compared to string floss in adults after a single use. The Journal of Clinical Dentistry, 24 (2), 37-42. PMID: 24282867 Free PDF: https://pdfs.semanticscholar.org/2fd8/4bd02e3ceb21d6faae988109a74a95c054a0.pdf
Sharma, N. C., Lyle, D. M., Qaqish, J. G., & Schuller, R. (2012). Comparison of two power interdental cleaning devices on plaque removal. The Journal of Clinical Dentistry, 23(1), 17. PMID: 22435320 Free PDF: https://www.researchgate.net/profile/Naresh_Sharma18/publication/221902011_Comparison_of_two_power_interdental_cleaning_devices_on_plaque_removal/links/541d09d00cf241a65a15ce3b/Comparison-of-two-power-interdental-cleaning-devices-on-plaque-removal.pdf