For my wife, I have now decided to use the S3 mini Value Edition. Why? It should definitely be a Samsung (as various other Samsung devices in the home are available), it should be small, easy to handle and is not high-end. Nevertheless, good performance and a (reasonably) Android updates with view updates.
The hardware differs mini to the "old" S3 by the fact that another processor is installed (ARM Cortex A9 Dual core 1.2GHz instead of 1.0GHz), an NFC chip in it and even Android 4.2.2
The performance is much better than the old S3 Mini. Everything goes liquid vonstatten.
The advantages of Android 4.2.2 over 4.1 are well known (widgets to lock screen, Apps Move to memory card), still some features that had the old S3 mini, including among others an automatic brightness adjustment of the display and Smart Stay (missing so the function is the active screen as long as the sensor detects the eye). Other features that can my mini S4 with Android 4.2.2 (battery indicator in%, ringer tone when the phone is in a pocket) can not the device.
Overall, however, to the price an absolutely great and really good beginner smartphone with built-in technology.