DB disk space requirements comparision between MySQL versions
One thing must be noted that you probably never realized: The setting of the option innodb_file_per_table will determine how much space is inside each database folder.

First, take a look at the InnoDB Architecture



Note the system tablespace (which was know is named ibdata1 in the OS).


In MySQL 5.0, the default value for innodb_file_per_table is 0 or OFF
In MySQL 5.6, the default value for innodb_file_per_table is 1 or ON
With innodb_file_per_table disabled (default in 5.0), the data and index pages for all InnoDB tables are stored inside ibdata1. When you create the table mydb.mytable, you get the following:


/var/lib/mysql/mydb/mytables.frm
Data and index pages for mydb.mytable are inside ibdata1

With innodb_file_per_table enabled (default in 5.6), the data and index pages for all InnoDB tables are outside ibdata1.  When you create the table mydb.mytable, you get the following:


/var/lib/mysql/mydb/mytables.frm
Data and index pages for mydb.mytable are stored in /var/lib/mysql/mydb/mytables.ibd



SUMMARY

Without setting innodb_file_per_table and just storing data


Databases under MySQL 5.0 will have nothing but .frm files for its InnoDB tables. Thus, you only have kilobytes of files in each database.
Databases under MySQL 5.6 will have .frm and .ibd files for its InnoDB tables. Thus, you will have megabytes or gigabytes of files in each database.