As you may already expect, they are typically easier to program and design with. Just have a look how many bypass capacitors you need around e.g. STM32F051 and a similar 8-bit micro.
On a hardware level, that's often true, although it usually depends on the pin count. STM32s are rather easy to integrate otherwise.
On a software level, that's a different story. Although the simplicity of 8-bitters may be less intimidating at first, their inherent limitations, especially regarding the memory models, can be a real PITA. Their limited ALUs as well. Some don't even have hardware multipliers or very limited ones (size-wise), which can make some computations extremely slow.
Typically, for a programmer that comes from the PC software world and wants to do embedded development, using a 32-bit MCU will probably be much simpler, at least from a programming standpoint.
The price tag really matters only if you make very cheap devices in large quantities.
As for power consumption - there are so many ultra low power 32-bitters these days that this is becoming a moot point unless you target ultra ultra low power (that you will find in only a handful of 8-bitters anyway) for very simple tasks. For more involved tasks, you may find that they spend a lot more time in run mode than a 32-bitter would, thus drawing actually more on average. So obviously, it all depends on the application, but the sweet spot may be hard to find before actually testing.
Other things to consider are the development tools, their quality, availability and cost.