[razzaj]

In fact http://www.bowyers.com/bowyery_longbowOrigins.php says the contrary to what you are claiming, and in their account of the Cercy battle they clearly mention how the longbow outranged, and out-powered the crossbow (look for paragraph "Crecy 1346: the Longbow's Finest Day").

Excerpt 1: "The crossbowmen had a lethal range of up to about 80 yards, and took up an initial position 100 yards from the English, in line across the field. Unfortunately for them they quickly found out that the longbow now had a lethal range of well over 100 yards. "

Excerpt 2: "They were shocked to find that the longbows could now penetrate French armour, and could also down the horses."

[lambda]

According to Wikipedia (https://en.wikipedia.org/wiki/Battle_of_Cr%C3%A9cy#The_Frenc..., and of course take with the same grain of salt applied to anything on Wikipedia, I don't have the sources on hand to cross check):

  The French army moved forward late in the afternoon, around 
  4pm after it had formed up. As it advanced, a sudden 
  rainstorm broke over the field of battle. The English 
  archers de-strung their bows to avoid the strings becoming 
  damaged; the Genoese with their crossbows could take no 
  such precautions, resulting in damage to their weapons.[26] 
  The crossbowmen began their advance, however they had left 
  their pavises back in the baggage train, and thus had no 
  means of protection as they loaded their weapons.[27][28] 
  The Genoese moved within range and discharged their 
  weapons. Damaged by the rain, the slackened crossbows had 
  little effect on the English line. The English archers shot 
  their bows in retaliation, inflicting heavy casualties on 
  the Genoese, causing them to retreat. The knights and 
  nobles following in Alençon's division, seeing the routed 
  mercenaries, hacked them down as they retreated. Froissart 
  writes of the event:

    The English, who were drawn up in three divisions and 
    seated on the ground, on seeing their enemies advance, 
    arose boldly and fell into their ranks... You must know 
    that these kings, earls, barons, and lords of France did 
    not advance in any regular order... There were about 
    fifteen thousand Genoese crossbowmen; but they were quite 
    fatigued, having marched on foot that day six leagues, 
    completely armed, and with their wet crossbows. They told 
    the constable that they were not in a fit condition to do 
    any great things that day in battle. The Count of 
    Alençon, hearing this, was reported to say, "This is what 
    one gets by employing such scoundrels, who fail when 
    there is any need for them."[29]

So, it doesn't sound like the crossbows were in pristine condition. Rather, their range was limited by the fact that their strings had gotten wet, while the relatively simpler (and easier to string) longbows were able to be protected from the rainstorm.