Ask HN: Which FB Plugin Is Better for Chatting (Message Us vs. Page Plugin)

Hey HN!

I'm trying to figure out which Facebook plugin works better for starting conversation with my website visitors. Facebook provide two different ways:

1) The "Message Us" plugin (https://developers.facebook.com/docs/messenger-platform/implementation#message_us_plugin) - this button sent the user user to Messenger (web or app).

2) The Page plugin (https://developers.facebook.com/docs/plugins/page-plugin) - It lets embed Facebook Page on a website and start conversation without leaving the site.

All these plugins can be represented as website widgets. There are some examples: 1) http://blog.jparkislandresort.com/ 2) http://www.band-brand.us/

Which way is better? Which widget is more convenient for the visitors? Thanks!