If you are comparing the size of your broker's data vs Tickstory, then that is expected. The size of the data export will be much larger when exported from Tickstory as it contains quality tick-by-tick information in the files.
If you want to save some disk space, you can choose only the time-frames you are interested in by selecting only those for export. For example, if you only test under the 15-minute time-frame, you can select only the "M15" during your export. (You can also delete all the other *.fxt files other than the EURJPY15_0.fxt one).
More information is available in the user manual if you press F1 within the application.