I wouldn't trust apps. Never do online banking over wifi.
Online banking apps are encrypted and authenticated end-to-end as specified by VISA and PCI-DSS. The standard is very tight, requires regular testing and independent auditing. That said, confidential information seems to be getting leaked on a monthly basis these days - as someone who works in that industry and sees it, the reason is almost always because money issues (i.e. Sears), overworked IT staff or clued-out management allowing a vulnerability to open and not be detected and fixed. CDN banks in my experience are very, very good at staying secured and take protection of confidential data very seriously. It's the retailers you have to be careful of.
As long as you are using the proper banking site and authentication occurs, you are safe. Obviously the key is to make
damn sure you are using the proper banking site and not a spoofed / phished site. Therefore it's best to either bookmark the site on your computer or manually type in the URL. Googling it, or responding to an EMail could result in a spoofed site.