Just how confidential is arbitration?

it depends. 

As with most aspects of arbitration, confidentiality rests with the parties. Yet, many arbitration agreements do not address confidentiality, and parties often struggle to amend their arbitration agreements once a dispute has arisen and battle lines have been drawn. 
In those cases, it is the governing arbitral law that, together with the applicable institutional rules, informs the scope of confidentiality covering that particular arbitration. The "confidentiality default" likely to apply under Austrian law is summarised below.

Arbitral proceedings and connected court proceedings may be private
Although Austrian statutory law does not contain any explicit provisions on the privacy of arbitral proceedings, such privacy is universally recognised and often implied in arbitration agreements. It is further fostered by Section 616(2) of the Austrian Civil Procedure Code ("ZPO"), which permits parties with legitimate interests to request exclusion of the public in court proceedings connected to arbitration. It is argued that since Section 616(2) ZPO provides for privacy in court proceedings connected to arbitration, privacy should be afforded, all the more, to arbitral proceedings themselves. 
Awards may be (partially) published
Even without the other party's consent, a party may publish the ruling or a redacted version of the award, if not the entire award itself. The applicable institutional rules may also contain provisions on publication. The Vienna International Arbitral Centre, for instance, may publish anonymous summaries or extracts of awards, unless the parties object.
Arbitrators are subject to a confidentiality obligation
Confidentiality obligations of arbitrators are universally recognised. They are derived from the contractual duty of care, laid down in guidelines and codes of ethics, and often implied in arbitration agreements. Arbitral institutions are generally under a similar obligation.
Parties may be subject to a (limited) confidentiality obligation
Neither Austrian statutory law nor case law expressly provides for a general duty of confidentiality. However, such a duty may be implied in Austrian law. Under Section 172(3) ZPO, if the public is excluded from a hearing, the content of that hearing may not be made public. Section 616(2) ZPO permits such exclusion of the public in the arbitration context. Therefore, it can be argued that Austrian law supports a general duty of confidentiality of the parties to an arbitration.
Nevertheless, even if such a duty existed, it would be subject to certain limitations. It would not prohibit disclosures required by law, challenges or enforcement of the award, or seeking assistance from courts in the course of the arbitration. It also would not prohibit disclosures to a smaller and closed group (such as potential purchasers), as only publications to "the public" are prohibited. Nor would such a duty prohibit the disclosure of at least the ruling of the award or a redacted version of it.

Can parties make their arbitration more confidential?
Yes, parties can and do influence how confidential their arbitration is. For one thing, parties should consider their confidentiality preferences when choosing the applicable institutional rules and governing arbitral law. The confidentiality provisions vary greatly by country. For example, the arbitral laws of New Zealand, Spain, England, France and Singapore recognise a general confidentiality obligation of the parties, while those of Australia, Sweden and the US do not. Naturally, choosing the right institutional rules and arbitral law requires sufficient familiarity with their respective key provisions.
Parties also can (and should) enter into confidentiality agreements. While confidentiality may at times be implied in a particular contract, relying on an implied obligation is hardly a risk worth taking. Parties are thus well advised to carefully draft tailored confidentiality provisions together with their arbitration agreement. For instance, these provisions could require that documents exchanged in the arbitration remain confidential, that witnesses and experts testifying in the arbitration sign confidentiality clauses, and, crucially, could subject breaches of confidentiality to contractual penalties.

Arbitrations, at least if seated in Austria, are likely to be more confidential than state court proceedings, even without particular confidentiality agreements. Nevertheless, parties are well advised to take the reins and include confidentiality provisions in their arbitration agreements. After all, it is up to them to determine just how confidential their arbitration will be.

Further reading

Disclosure in Austrian civil proceedings
Commercial mediation - confidentiality matters