The advantage of drip is that it can put water exactly where..and ONLY where it is needed, right at the root zone of plants. So you avoid putting a lot of water on mulch or other areas which just need no water at all. It also eliminates overspray common with sprinklers, no matter how carefully you lay out the heads.
It is not a good idea to mix drip on sprinkler zones, due to the timing issue as you mentioned, but multitube take offs , etc, can still make this better than sprinkling.
Micro sprinklers are good for small turf or ground cover areas which need broadcast water, but not too much.