They have set a minimum rate that a country must set VAT to avoid one country undercutting the rest. But the range is broad. The bigger economies like the UK, France and Germany have very similar rates at 19-20%, while the Scandinadian countries are more like 25%. Raising tax cuts demand, so countries like Germany would not accept a 25% rate.
EU harmonisation could affect the exemptions to VAT. We currently have a long list, bigger than most other countries. The EU could try to cut our exemptions.