It all depends on your exact requirements - IF you can, sleep mode is by far the best option, and the Pro MIni is a far better choice than an Arduino Uno, as the Arduino board has too many other items wasting lot's of current.
Personally I use PIC's for such purposes, as they are fairly optimised for low power usage - and I'm usually looking for 5-10 years battery life.
You usually need to be looking at average current consumption below 100uA to get really long life, and special batteries as well (shelf life is often less than 5 years).