A Sidewinder Missile costs around $450k a pop and the balloon and the intelligence it holds return to earth at terminal velocity destroying everything. A couple of 20mm rounds through the envelope however would see the balloon descend somewhat slower towards earth thus preserving the tech attached for the boffins to get their teeth into.
What other race in the world would plump for total destruction by missile when a few small calibre rounds would do the trick more efficiently? Yee Haa!