This ban is nothing but a pr-stunt, mainly by the conservative party, to appeal to the "swing-voters" that drift towards the right-wing FPÖ. It was part of a deal the two ruling parties - socialists and conservatives - negotiated to bring the government back on track and prevent reelections. it has nothing to do with a stricter separation of church and state (crucifixes are still hanging in all/most classrooms of public schools) or security reasons. there are almost no "burqa-carriers" in austria - when I lived in Graz, the 2nd biggest city, I saw one or two each week... and I lived in that part of town that is the hotspot for immigrants.
i also used to live in london and worked in the east end for a while. every sunny day, with the street market open I'd leave the tube to enter a street full of burqa-(or whatever you call the version that doesn't use a veil but a ninja-slot for the eyes)-wearing women. honestly, it was weird at first (because almost noone wears them in austria!) but I never felt unsafe and to my knowledge no burqa-wearing woman has used her "disguise" to commit an act of terrorism in the UK yet.
AFAIK the streets in front of the royal london hospital are still roaming with burqas till this day - and rightfully so.
I do believe the world would be a better place if everyone kept their religious symbols covered and prayed at home without preaching in public, but that's not going to happen anytime soon.
Banning a piece of clothing does not ban terrorism and Kurz & Co know that. In it's core this is not a ban targeting muslim women, but swing-voters leaning towards the right.