Their webs can get to be about the length of two buses and can easily bridge rivers without even giving a shit. In order to support the weight of all that web and the struggling, dying life-forms caught in it, the webbing has to be incredibly strong. In fact, it's one of the strongest materials known to man -- 10 times stronger than Kevlar.
M. Kuntner, forskning.no
Which might make it more suited to downing small aircraft than birds.
Of course, up to this point, the spiders have only been using their horrible science to build adamantium webs, not suits of armor. But it's safe to assume that this is only the beginning, and pretty soon we're going to need better bullets.
Huh. Apparently Spider-Man can beat Batman. Thanks, Nature!