Many years ago (I believe it was regarding Platform 5) it was said that it would improve performance to check if a list is empty by asking if Length = 0 rather than using it's property Empty.

However after many years this property remains which makes me think if the statement above is correct. In my view of the things both have same performance (not like the count which makes the query to be repeated).

Any thoughts on this topic?

If you use Length, I think platform is not able to optimize the query, as it must fetch data, or the list length will always be zero, as it represents the number of records in the list. 

If you only want to know if there is data or not, use Empty. The aggregate will be optimized and no actual data will be fetched.