The Austrian EHIC card provides “medically necessary” treatment in state-provided healthcare during a temporary stay in any of the 27 EU countries, Iceland, Liechtenstein, Norway, Switzerland or the UK.
The UK EHIC/GHIC card has similar coverage in Austria, but please remember it is NOT an acceptable policy for permanent residency purposes. Also when you become permanently resident in Austria, your UK EHIC card is no longer valid (unless covered by a UK S1)
Please also remember it is NOT a substitute for adequate travel insurance (e.g. does not cover repatriation, helicopter transfer to a hospital following injury on a ski slope).
An EHIC card also is unlikely to cover any Private Healthcare treatment including ambulances.