Ok a bit more data etc.
On Crossbows.
Here there is a big blank spot. There have been a lot of studies and amateur testing done on pretty authentic longbows in the last ten years or so, there has been a ton of testing done on armor most notably by Mr. Williams but there have also been several other studies.
There have also been studies done with firearms and armor directly.
But with crossbows there is a blank, mainly because we don't have many crossbows equivalent to those used in the 14th-16th Centuries available for testing. Alan Williams mentions one semi-formal test of a 1200 lb draw antique but detail was scant other than it shot a bolt 450 yards. Most of the antiques which still survive may be too dangerous to test with after 500 - 600 years, and there are only a handful of people around today who have the sufficient knowledge and skill to forge prods capable of the 800 - 1200 lb draw weight of a Renaissance heavy arbalest.
However I have been advised by a smith in the UK that he has a client who recently ordered a 950 lb crossbow specifically for testing, hopefully they will do a good well documented test on some realistic armor and then we will know something further. At this point I don't even know what the energy of a 950 lb crossbow is or how it compares with a longbow or a musket.
http://www.aiacrossbow.com/crossbow/exomax/
I know modern hunting crossbows of between 150 and 220 lb draw generate between 120 - 150 joules depending on the quarrel used. I assume a 1,200 lb draw arbalest would be significantly more powerful than that but various other factors like the span distance (short on most antique crossbows) and size of the prod all factor into the power of the weapon. Crossbows do shoot a bolt about twice as heavy as the arrow shot by a longbow. How powerful were Renaissance crossbows? We really don't know at this point. In the heydey of plate armor in the 15th Century, they apparently considered crossbows a significant but not insuperable threat. Italian armor of this period was proofed at two levels, for the 'little crossbow' and for the 'big crossbow'. The latter was a higher grade of armor (the top grade).
On Firearms
Here is some more information from 'Knight and the Blast Furnace':
from Chapter 9 of Williams' book, p. 942 - 948
1.9mm wrought iron plate requires 900J from a steel ball or 1500J from a lead ball to defeat it.
2mm of Good quality tempered steel armor can resist about 1800J from a steel bullet or 3000J from a lead bullet.
An average quality 4mm iron cuirassier's breastplate (17th century) would need 2000J to defeat it.
There were also up to 6mm thick iron cuirasses in the 17th Century and special laminate cuirasses made from 2mm of steel and 3mm of iron. These were apparently very effective but I don't have any data on them yet.
From p. 945
a Hussite 15th C handgun with serpentine powder produces 500-1000J at the muzzle.
early 16th C arquebus with serpentine powder produces 1300J at the muzzle
the same weapon with corned powder produces 1750J
later 16th C musket with serpentine powder produces 2300J
the same weapon with corned powder produces 3000 J
Bringing in modern firearms* based on this wiki on
Muzzle Energy,
.357 Magnum revolver with a 6" barrel 750 Joules
.44 Magnum 1400 Joules
Ak-47 (7.62 x 39mm) 2070 Joules
FN-FAL / M-60 (7.62 x 51mm) 3799 Joules
.50 Cal BMG 15000 Joules
*Of course this is all potentially different depending on the ammunition and the barrel length.
One of the interesting things about all this to me (if it is correct) is how powerful 16th Century muskets got, they were comparable in muzzle energy to an Ak-47! Of course bullets from modern firearms also retain their energy much longer than Musket or Arquebus balls do and modern bullets probably penetrate better. The stats on the armor make me wonder if a good 15th Century harness could stop an Ak-47 bullet... I wish I had some tempered steel armor that I could shoot at with an Ak-47 or a .357. (I wish I lived on my own island with Scarlet Johansson too.) Also, I wish I had a .50 caliber machine gun I shot one once in the army those things are bad ass.
But this does seems to support the opinion of [ame="http://www.amazon.com/Armourer-His-Craft-XVIth-Century/dp/0486258513"]Charles Ffoulkes[/ame] that regular plate armor is capable of resisting the firearms of the 15th and early 16th Century. It's only in the latter half of the 16th century that armor is seriously threatened by firearms. This is why Muskets were originally considered special armor-piercing weapons, used alongside smaller arquebus for a long time before the two weapons kind of merged together (the musket got smaller and gradually replaced the arquebus).
Of course even if your armor made you relatively safe from firearms, there was no armor in existence which protected you from cannon fire, and horses could only be partially armored at best (never on their legs for example) so the value of armor was in decline.
But armor clearly had a great deal of value and looking at this data you can begin to understand why so much very high quality armor was produced during the Renaissance at so much expense in spite of the presence of large numbers of recurve bows, longbows, crossbows, halberds and firearms including pistols, arquebuses and hand-culverins. In some 15th Century battles tens of thousands of soldiers fought in heavy armor, to fight without armor protection in this time period meant almost certain death.
G.
I think there is more data to emerge on this subject, and there may never be a definitive answer about which style of warfare had more merit.
