Have a look at the the permissions being asked by these Andriod Apps. What do you make out of these snapshots? Which App is more secure - not from the point of view of security for the App but security for the user who downloads and uses them. The one on the extreme left(first one) is likely to have more access to your device than the other two. The makers would argue that these permissions are required for the features and functionality of the App. The question here is who will decide how much permission is required and who will guarantee that these permissions would not be abused. The one on the extreme right-bottom is more trustworthy as it requires no special permissions. But how many of us really pay any attention to such details?
Unlike the applications on a Desktop, with mobile apps it is difficult to find what they are really doing behind the scenes. The situation is compounded by the fact that the mobile devices contain enormous amount of personal, sensitive and financial data. The email apps are always online.The device is always connected to internet in most cases. The passwords and others credentials are just there begging to be stolen away.
Personally i prefer to use my browser on my mobile to access the various web sites and web applications rather than download an App. Re-entering usernames and passwords every time you access an web application or a website should not bother you if your are worried about safety of your data and online identity.
Having written what i wanted to convey, i would like to clarify that i am not aware that the above mentioned Apps are untrustworthy in anyway. I just picked them up for an illustration.