i have been reliably informed that you can get about 100fps on simple animations, and about 30fps on complicated ones... this is assuming 256 leds in a single string (like these things technically are)
The refresh rate doesn't depend on the host CPU unless your animation needs a lot of processing power (eg. decompressing a video).
The usual bottleneck is the WS2811 chips inside the LEDs, they need to be fed data at about 800KHz, no faster, no slower. It doesn't matter if you're using an AVR or an ARM, the strip refresh rate will be exactly the same.
256 LEDs will take 7.7 milliseconds to update (call it 8ms because you'll always have some small losses because of loops, etc.). If you can update your animation in 2 milliseconds then you'll get 100fps update. To get 30fps you'd have to take 21ms to update the animation, that's 1300 clock cycles per LED on a 16MHz chip, which is a lot of processing...
All that aside, those things are cool...! Who cares if there's an AVR or an ARM driving them?