AVRs have much better sleep modes (single digit microamps) and predictable performance (to the exact clock cycle) by default. If you need long battery life or hard real-time performance then they're probably a better choice than the Raspberry Pi.
All reasonable responses in this thread to GP, but parent hits the nail on the head.
For non-hobbyist problems where you really need a microcontroller, it is selected by spec (in terms of performance, operational predictability, physical/material properties, power consumption), and then purchased in volume (~ millions). Employing a general-purpose CPU for said problem, while potentially alright when prototyping, would not be satisfactory.
True, however that's AVRs and not Adruino. You very quickly get out of arduino-land when you have any constraints like battery life or performance. By far the vast majority of people contemplating either Arduino or RPi will never know enough to be able to tune things like that.
Heck the last time I looked into doing sleeping on an AVR-based Arduino it basically said go look at the 328's manual to set the registers directly. (Although that was a long time ago.)
One abstraction layer above in fact. It's like saying a farm tractor and a pickup truck are the same thing because they both can move you from point A to B.
They're not the same thing, but unless you have some specific use case that demands a farm tractor and you concretely know why, you should go for the pickup truck.