OK, then I will argue that the Wars of the Roses, ie the dynastic in fighting between the so called Houses of York and Lancaster can be traced back to Henry IV's usurption of the throne and deposition of Richard II. so say, the Battle of Shrewsbury in 1403- does that give you a satisfactory overlap?

Darrell.

... and they ended with the death of the 'de jure' Duke of Suffolk at Pavia in 1525.

This thread has been a very interesting discussion, which I've been enjoying, but not contributing to so far. Despite all of the varying viewpoints it's very difficult to point the finger at anyone and say you are right/wrong.
However I will offer the following points for your consideration;
a) At point of impact a bodkin-headed warbow arrow exerted the same force as a crossbow bolt, over the same area, while requiring around a tenth of the draw weight. The longer draw length and weight of the head (typically twice that of a bolt head) being the compensating factor.
b) Typical effective ranges of both weapons tended to be similar... with 300 yards being the 'typical' effective range and less than 100 yards being the optimum distance where both weapons were at their most efficient.
c) Except when the expense was waived, mass-produced arrow and bolt-heads were made from iron and not steel. Some have been recovered which have 'curled' or 'bent' upon impact with presumably superior quality armour.
d) On good-going a fully-armoured knight could cover 300 yards in just under three minutes, albeit at around 100 lbs of armour, he would have required a massive amount of energy to do so (2x more - much more than that required to carry a 100 lb pack in fact - try moving your legs with 8 kilos attached to them!).
Moving at a slower pace would help, but exposes you to more shooting. Armour sapped energy at alarming rates; you've also been wearing it for hours before you even set off across that field.
Mounted knights obviously move much quicker and if it is barded, their mount 'carries' its own armour, rather than 'wears it'. Even at a sedate 20 mph, a mounted man covers 300 yards in half a minute (how many rules give cavalry 5x the move of infantry?).
e) Improvements in steel making were used to make armour lighter, as much as they were directed towards improving protection. Spiralling expense produced fewer and fewer customers, to the point that by the 1480s, there were gentry in France serving as archers, as they could not afford to buy what was needed to become gendarmes. By the early 16th century, the archers were all gentry.
In England too the former one-size-fits-all class of men at arms (or spears), becomes divided between the remaining fully-armoured 'spears' and part-armoured 'demi-lances'.
Iron 'munition' armour is much cheaper than the latest steel types, but is around twice as heavy (or half the protection if it's the same thickness). If you imagine you have maybe a quarter of your men in the latest gear and the rest in iron, imagine how hard keeping them moving at the same speed must be, especially with the hotter heads itching to get into the fight..
f) The warbow is not 'typically' English and North of the Loire in France, the crossbow was confined to the gentry for hunting and town militias (who were typically middle class). There were some 4,000 archers in the ordonnance companies raised in 1445, roughly the same number that the English had at Agincourt.
g) English archers of the HYW were picked men and tested for their ability before they drew pay. Archers in the WotR were men with bows, raised, marched off to war and God willing, back at home before a month or so had passed. They belonged to a society in which the levy had not been raised in anger since 1403 and musters tended to be more of a lad's day out than preparation for war (the northern shires excepted).
h) Despite the massive numbers of archers that could be potentially raised during the WotR, the era saw the return of English cavalry. Indentures as early as 1492 show 'spears', 'custrels' and 'demi-lances', along with rapidly reducing numbers of mounted archers. This is hardly what you would expect from a society in which the longbow was 'Queen of the Battlefield' and a decisive weapon of war.
Okay that's enough I think. The bulk of the longbow myth comes to us from an artillery officer's faith in his arm of service as being essential to victory, so he portrayed them as the QF 18 pdr gun of his day. It is without doubt an excellent weapon, comparable to the average crossbow, albeit with a higher rate of fire... however you can't hand out a longbow and tell a guy to go out and fight, you have to nurture your archer pool.
It was not a battle winner- the French always made it to the English line (albeit they would be knackered) and it all came down to handstrokes. Stakes, pits, blood and mud all contributed to French defeats as much as the longbow did. We also tend to forget that the French actually did win quite a few battles and ultimately the HYW; the English still had their longbows, but it was leaders they lacked.