And if you're using something bigger, like a Raspberry Pi, you would use Linux anyway.
(But people are using it, so it must be useful. I just don't imagine the kind of applications...)
This sort of OS is very useful in situations like wireless mesh networks where the code is more complex than would be suitable for a super-loop architecture, but the system is too resource-constrained to run something like Linux because it is trying to hit power requirements.
the hardware abstractions look like they allow you to reuse application code with different hardware drivers too, which is nice.
It mostly fits for people needing exotic mesh networking and not much else. "Much else" would imply just running it on a Pi.
If you want to play with the hardware you have to bite the bullet and get used to device costs being 2 to 10 times the cost of microcontroller or Pi unit costs. Contiki hardware is extremely expensive.
If you want to play with the software run emulators / simulators with contiki on desktop hardware, this cost is basically free (other than 100 watts per desktop etc).
If you want to play with mesh networks the best bet is something like WRT54GL with ham radio mesh software on it aka HSMM for $50 per node (at least its $50 Amazon Prime delivered, maybe more or less for you)
There's the rub. I've seen Arduino's be turned into real development environments, with a keyboard and mini-display, and onboard editor for Assembly, to boot! So I don't think the Arduino is 'mini' in any way; maybe the demo's of Arduino you've seen are one thing, but actually the Arduino is a kick-ass machine. Some people treat them like an Atari. :)