I have experience connecting sub's to receiver subout connections (which uses receiver's crossover) and via receiver main-in/pre-out connections (which uses sub's crossover). For most powered subwoofers, the trade-off of getting a lower crossover and using your mains better low-end capabilities versus having a (usually) higher crossover built-in the receiver is volume control convenience. Many subs do not have a remote control, though most do have a volume knob -- when using the sub's crossover, for music, you'd likely have one sub volume setting, though for action movies, you'd likely want to turn-up the sub volume a bit for thos explosions. When using the receiver's crossover, you can control the sub's output setting via the receiver's remote control. Convenience versus potentially better sub/mains blending.
