A Propeller has multiple CPUs which allows it to do multiple tasks much faster than most standard microcontrollers can multitask, since they must run all tasks through one CPU. That's its claim to fame. For example it can output a video signal while also doing other tasks. It's useful for fast multitasking requirements such as multiple axis robots. Being able to write code for each processor independently can simply multitasking programming. You don't have to worry about handling interrupts and storing any intermediate data when switching tasks. Multitasking with a single CPU generates a lot of overhead..
Not at all. Most robots- multiple-axis or otherwise- would not be controlled by a multiasking CPU. You'd typically line up the tasks in a row and do them in a row; this is like day 3 of a microcontroller course. There's no need to complicate this as such. And interrupts aren't THAT inefficient. Under normal circumstances, often you could handle them with <1% of processor time. Plus, once you go with like a dsPIC33F, they use DMA so a peripheral can load up or read out of memory without ever needing a CPU cycles.
And it's a strange line of thinking to ask "which is faster?" I'd only care "Can the PICxxFxxxx do the job I need to my spec?" In fact, about 3/4 of the time you SLOW DOWN a PIC below its max clock, or employ Sleep mode, because there's no use for more speed and it'll only take up more power. And I'm not going to employ a dsPIC33F because it's "fast" if a 12F can do the job for less $ and much less mW of power. These are not sports cars. A TV remote employing a processor that is 1000x faster than the job needs is not all that impressive. Sure, if we add a color LCD and voice recognition, I'll bite, that'll be kinda cool. But just having a remote which is an "on" button and 1000x too much capacity is kinda foolish. In fact, the kick-ass part is when someone does something remarkable with a low-end 8-bit like a 12F by being clever with assembly. That impresses other engineers and impresses cost-conscious bosses far more.
Generally, you would not select a chip because someone said it was "fast" then look for a task. You start with a task and find out what will fill it.
As designers, there's a lot that makes a chip interesting and "impressive". Speed is one. RAM and program space are others. On-chip peripherals, like ADC, SPI, serial, comparators, PWM, USB, CANbus. The ability to bootload (self-program). On-chip EEPROM. The ability to Sleep on nanoamps of current. Taking only microamps to run. The ability to run on very low voltage or Extended Temp Range. A powerful instruction set. 16 bit instructions. DSP core. An available C compiler. A
GNU C compiler. Product availability/support. Pincount. COST.
Honestly? The multiple-controller thing? I don't even see what it does that can't be done just as well- generally better- with a PIC or Atmel, the "inability to multitask" as described never existed. They do just fine at it. They excel at it. And from what I can tell they're not nearly as fast in performing tasks as claimed compared to modern, advanced controllers. For one, you cannot "add up" the power of the cogs like this for a sum. No one cog can handle over 20MIPs and due to timing requirements between them, some will be better utilized than others. If I have one 20MIP CPU running as a PWM, one as 300 baud serial and one doing actual program, that's not 60 MIPs.
And MIPs are not a good measure, an advanced 16-bit core with a smart instruction set designed for DSP for example can run 50x faster at a 16-bit DSP task than an 8-bit controller using the same MIPs. From what I can tell the cog CPUs are fast but extremely basic. More of a question is that, since Propeller uses a "high level language", it's going to be difficult or impossible to make code that very specifically exploits the capabilities of a core. I've tried to find out what a cog actually IS, its fundamental capabilities (like instruction set), and have never been successful at finding that information. I keep getting redirected back to "SPIN", and found only mention that an assembler "PASM" does
exist, but found no actual information on it. Not a good sign.
What the Propeller DOES have is some hardware which makes it unusually "friendly" for video generation with few external components. People have done some video generation with PIC but it is quite taxing and seems to require significant external circuitry. Either way, neither one has anything like a color frame buffer here. And if the demands of generating video and running other tasks are too high, it's not a problem to run the video generator on a separate chip and talk to it through serial or SPI.