I've used microcontrollers many times, and the Arduino is a useful prototyping thingy when you want to play with them. When you are into (analog) electronics, a microcontroller is luxury; when you come from PCs, it's primitive, but there is a lot of fun to be had by doing things with the minimal amount of code in the fastest way, all the while counting clock cycles 8-).
The Raspberry Pi is huge overkill for many applications, and it has an enormous power consumption. I build things like MPPT for small-scale, portable solar energy applications, and the controller should ideally use less than 2mA. Even for doing sensor integration a microcontroller is powerful enough; here's a link to one of my projects.
The Pi is not too bad at a couple of watts, unless you want to run from batteries. Certainly better than running a normal PC if you just need a simple server. I have ideas for projects that could use an Arduino. Need to get hold of one and experiment when I find the time.
A couple of watts is huge! It depends on what your reference is, I suppose 8-). My last design for a portable solar battery charger uses under 10mW ...
I'm using a Pi to run my home automation and I think it uses less power than the old system (Cytech Comfort). Running a whole Linux stack is overkill for a lot of application.
I may be setting up a solar system some time. Looking to build a garden shelter and solar could do the lights for that. I'll have to think about what other features I could incorporate.
For small applications, this may interest you. It depends on your power needs, of course, the chip mentioned outputs a max. 2A into the batteries, but the way it works is brilliant, a kind of poor-man's MPPT. Should be implementable using a microcontroller.