I can't find a study coming to the conclusion that firearms result in a higher percentage of unrecovered wounded deer than archery, but I would read one if found. The two below are the most cited studies for archery. I also can't find a pure firearms study but a 18-50% loss rate for firearms would shock me--I'm hopeful it's much lower. Many of my friends and co-workers hunt and the topic of losing a rifle shot deer rarely comes up while archery losses are talked about frequently. It's not empirical...just my observation.
To me, if the end goal is a deer in the freezer, why not do it as quickly and humanely as possible leaving as little as possible to chance without worry about "tradition" or "cheating". I think that is the debate going on in this thread.
Modern archery:
http://www.seafwa.org/pdfs/articles/Pedersen-31-34.pdf During the 1989–2006 hunting seasons, 104 bowhunters failed to recover 162 of 908 deer hit by arrows or crossbow bolts, corresponding to an 18% wounding rate.
Traditional archery:
http://wp.auburn.edu/deerlab/wp-content/uploads/2014/05/581998-SEAFWA.pdf
Of the 22 deer shot by archers, 11 were recovered by the hunter, resulting in a 50% wounding rate (deer shot but not recovered).
Yikes! Really?