It all depends on how you work. But the basics are this: muting the sequencer will save a little CPU as no notes will be "fired". Muting from the mixer won't do this, but you do have some advantages to muting in the mixer - when you un-mute, the audio will already be playing. Compare this to un-muting on a note track, which won't make a sound until the next "note on" is encountered in the time line.
For long sustaining sounds like with a long reverb, pressing mute in the sequencer won't necessarily mute the audio right away.
Long story short: one is muting "data", and the other is muting an audio stream. One can be automated (audio mute), the other cannot.
Signal flow wise, the sequencer mute comes "first", and the audio mute (almost) last (the master section follows any audio mute in the signal path). Going back up the signal path even further, you have "clip mutes", which come before the sequencer mute. Reasons for muting clips are to test arraignment ideas, etc.
"Creative" use of sequencer mutes is more limited to alternate takes, or alternate edits on a track, while creative audio mutes have many applications from rhythmic gating to using them to switch between tracks (muting one while un-muting the other), etc.
That's all I got off the top of my head…
