I think the types of things ITU would want to assert control over are centralised functions around standards development and name allocation that are currently carried out by ISOC and its parts (IAB / IESG / IETF) and by ICANN and its parts. Both the Internet Society and the Internet Corporation for Assigned Names and Numbers are not-for-profit organisations that are not directly under the control of any government (but which are incorporated in the United States, and so are subject to US law).
From a purely democratic perspective, ITU, a public body that forms part of the United Nations, and ultimately controlled by governments worldwide (many of which are democratically elected) could be viewed as a more appropriate body to handle the centralised functions than private bodies in one particular country.
In practice, however, international government can be a very bad place to start from when it comes to standardisation, because politics can get involved to a much greater extent, and everything gets slowed down by excessive governance process which becomes a burden - ITU standards are being superseded at a faster rate than ITU can produce them.
Obviously, the EU / Pirate Party might also be concerned that the ITU would want to assert control over more than ISOC / ICANN currently do.
ITU control is not about standardisation, piracy, or governance. As with everything, its about money and power. Oppressive governments want to de-anonymize users & enable greater censorship. Poorer countries want to charge for data transmissions - ostensibly to fund their own internet build outs.* Europe's ISPs want to tax the large American internet companies.
* These same countries profited by charging international calling fees which have been greatly reduced by VoIP. Many of them have corrupt governments who use these fees as a source of international currency.
The context for this is the World Conference on International Telecommunications 2012 [1] to be held inn Dubai in December. A major purpose of the meeting is to consider updating the ITU's International Telecommunication Regulations (ITRs) [2,3] to include an internet governance role for the ITU.
Its not very clear what the detail of the proposed changes actually is, but the Internet Society have a summary [4] that suggests a takeover of technical standardisation efforts (e.g IETF and maybe W3C processes), the regulatory functions of ICANN/IANA, and maybe oversight of the regional IP registries.
One point of view is that this is a power grab by the ITU, who see this as a last chance to remain relevant as the networks they used to regulate (traditional voice and data comms) are absorbed by the Internet. Behind it are various ITU member states (principally China and Russia) who hope to use an enlarged ITU as a proxy to control the Internet to further their domestic and international agendas.
From a purely democratic perspective, ITU, a public body that forms part of the United Nations, and ultimately controlled by governments worldwide (many of which are democratically elected) could be viewed as a more appropriate body to handle the centralised functions than private bodies in one particular country.
In practice, however, international government can be a very bad place to start from when it comes to standardisation, because politics can get involved to a much greater extent, and everything gets slowed down by excessive governance process which becomes a burden - ITU standards are being superseded at a faster rate than ITU can produce them.
Obviously, the EU / Pirate Party might also be concerned that the ITU would want to assert control over more than ISOC / ICANN currently do.