To the native English speaker, there really isn't a huge difference. They have the same meaning and same implications.

In your example, the present continuous is considered a future plan with arrangements (Monday evening). For future progressive, it's a fixed future event. Those are just fancy ways of saying that you have a plan to meet John on Monday evening.

The smallest difference to me is that "I will be meeting John" sounds like you don't see John very often, whereas "I am meeting John" sounds like it's something you do frequently. This might just be my perception, but that's how I interpret it as a native speaker.

Hope this helps!

There is no difference in meaning.  You can use the present progressive to mean the future.

We are going to the zoo tomorrow is actually more common than We will (We'll) be going to the zoo tomorrow.