Every Sigilyph I've gotten only had Psychic attacks. Dark types wall every Sigilyph set I've come across. Also, pretty much all Sigilyphs have Psycho Shift but not all of them have a Status Orb, rendering the move near useless. It's also murdered by dark attacks. Zapdos is killed by rock and ice type attacks but most of the pokemon that carry those moves are weak to Thunderbolt (Articuno, Aerodactyl etc). And for some reason, Zapdos has Lightningrod despite it not being released yet. Most of the Pokemon that beat Zapdos can't beat it when it's behind a substitute, a move which is present on nearly all its sets. And considering the number of grass types and flying types in this metagame, it's extremely easy to set up a sub.
Sigilyph is obviously more threatening if it's accumulated lots of Cosmic Power boosts but it can still be easily phazed by Skarmory, and can't get past Dark types such as Bisharp and Mandibuzz. If you're one of the lucky ones who got a Sigilyph with an attack other than Stored Power, you should be very happy. Zapdos is much harder to stop than Sigilyph in most cases, but if you lack a Sigilyph counter you're almost guranteed to lose.