Send Message Pro:
This is great for animation that requires trigger once, such as bomb exploding, card flick etc.
Very light on the network, since the data is sent based on trigger.
Flexible to customize your animation.
Send Message Con:
For a rapid animation update, the animation might be a bit jerky and sometimes doesn't not trigger accurately, which can happen to fast-paced games.
To mitigate the fast paced animation issue, developer can create a system that collect animation triggers in string format, this way you can send the animation state for every 0.5 seconds if the string is not empty. However, this is a con because this is vary hard to do and quite troublesome to get the logic.
Instance Variable Pro:
This is great for animation that is bounded by movement and object with position updates (such as bullets, rockets).
Very easy to setup and implement. The instance variable itself can be used repeatedly in peer to create customized condition for customized animation.
Instance Variable Con:
To many sync can cause heavy load on the host and congesting the network.
Not flexible if you want to create custom animation since you can't make use strings to the limit.
Conclusion
MP is very different from the normal workflow that you see in single player games, so try to learn it from the basic functionality and make sure you can understand what each action/condition does. Never forget that due to the scarcity of MP users at the time of this tutorial is being written, you have to rely on the manual and your creativity to get things right, throwing vaguely described question might not help anybody at all.
Try to make some capx yourself before asking question in the forum because the question of MP is not easy to guess from just description, screenshot and even the capx itself! Having said that, providing capx along with your question is always best because the community can trial and error from you capx rather than speculating theories which are not proven. Help us to help yourself.