The question really comes down to the context in which we use these two constructions.
Typically, we say things like:
I will be finishing the lesson around six so I should be able to meet you shortly after that.
The speaker looks ahead to a likely situation in order to make a subsequent arrangement.
On the other hand, the future perfect tense is one that people use to imagine that they are looking back at an event that still lies in the future. It's a way of picturing future events as if they have already taken place. So they say things like:
By six o'clock I will have completed the exam.
By the end of the year my military service will have finished.
By this time tomorrow I will have arrived back home.
So while both constructions are common, they tend to be used in different situations.