My quick two cents are following.
1) I would oppose an EU bank guarantee on the basis that I oppose all government guarantees of bank deposits. It perverts risk taking with people's deposits and puts taxpayers on the line for private losses. The best solution is to scrap all bank guarantees. Bank runs and the threat of them are a very good thig as it forces banks to be more prudent.
2) The reason it is so difficult for people to open accounts in other EU countries is because of all the regulations already in place. If a banking union means less regulation then I am in favour of this, but anytime a government body does something by it invariably introduces new and more laws. You can't solve unintended consequences of one regulation by introducing another one.