Advantages:
The asynchronous mode of replication is faster than synchronous mode. With the reduced latency, it offers a better choice when considered for use in a reporting environment.
If the replication involves complex topologies, the asynchronous mode is far more simpler to configure than synchronous mode.
The asynchronous mode is more effective than synchronous when it comes to tolerance due to network glitches, database issues on the target databases as well as stopped processes in replication. For it does not hold up the source database during such glitches.
Disadvantage:
The asynchronous mode of replication is more prone to data loss than synchronous mode.
In an environment where the transactions are concurrently executed by customers, etc, on all nodes, both the modes offer their own advantages and disadvantages.