A decent ligature can make a sizeable difference to your sound and responsiveness from your reed and mouthpiece. When comparing between a basic brass ligature and any of the more premium products, the difference you can feel in both playability and comfortability is staggering. Material ligatures like Rovners and Silversteins work very well with metal mouthpieces. Metal ligatures can be more fiddly to use, but they release the upper frequencies and let the reed resonate very freely, which works especially well with stuffier, darker mouthpieces.
Aurally, the differences between the ligatures are going to be very slight, but the feeling and response from the reed will vary wildly.