Do I have to pay VAT if my company attends an event in another EU country?

Yes. Events in the European Union are subject to VAT in the country where they take place. For a more detailed explanation, please see the "Supply of services" section in this article by the European Commission. It states:

B2B services in respect of admission to cultural, artistic, sporting, scientific, educational, entertainment and similar events will be taxed at the place where those events actually take place.

Example 34: When an Irish company for business purposes pays for the entry to an opera in Verona, the ticket will contain Italian VAT. That applies whether the ticket is bought on-line or at the ticket booth.

Example 35: For a conference organised in Stockholm for participants paying a fee to attend, Swedish VAT is charged.