dsPICs run at 30MIPs. That involves some complex 16 bit math and some powerful matrix operations, and FAR more RAM.
There's no reason whatsoever that a dsPIC or any uC can't perform many tasks at once. OK it can't execute two instructions on the same cycle but dividing up processing power among tasks is very common. Hardware resources can do many useful on the same cycle as code executes.
The Prop can run much faster, but the ops and memory are limited, and the way it shares the bus is also potentially limiting. It's hard to understand what this will be advantageous for.
I kinda think the Propeller might be a router or something where it needs to run at really high speed but do little work. Still I'm not sure. Maybe some low-level image processing??
The thing is, Parallax ain't exactly some ultra-high-tech company. They repackaged the PIC into a very weak product that has no serious industry uses, just high school stuff, and then spent a TON of money on marketing.
So I'm kinda skeptical that they made something new and remarkably useful. One theory, it's a device that has virtually no use whatsoever but has features they can confuse people with as being something "cutting edge" and sell to schools.