The earliest comparisons between the crossbow and handgun were written by Paolo Santini and Lampo Brago in 1452 and 1454 respectively. Brago's book is called Strategicon adversum Turcos.
If any Italian-speaker here could find and translate the relevant passages I would appreciate it, and many other anons would probably also be interested in reading it.
Here's what is said on the two manuscripts in A Bibliography of English Military Books Up to 1642:
"Paolo Santini may be said to be the first writer on artillery; his MS., which dates from the year 1450, containing drawings of ordnance, powder mines, and receipts [sic] for fire-balls and hollow balls filled with powder; while Lampo Brago is the second. The MS. of the latter, which was written in 1454, is the earliest known treatise exclusively on artillery, and contains and interesting comparison between the crossbow and the hand-gun.* Like Santini's, it has never been printed [as of 1900].
*Promis. Santini, in 1452, uses the same arguments in favour of the bow as Smythe uses in 1590."