It would of been interesting to see if those two different containers played a more funtional role. Lets say Safes are harder or completely safe (no pun intended) from robberies that could take place in your home while chest can be broken into, resulting in you tracking down the robber & or doing something to prevent future robberies of your home, just like a random encounter.
Safes would be able to protect your items because of the lock mechanic. However the chest just have a normal lock on them so it would be easy to open with a lockpick. You could easily smash the lock in real life
I have Hearthfire, and it makes my OCD happy that I have so many containers to arrange my stuff in, as well as all those weapons racks to show off my weapons instead of putting them in a container where they wouldn't realistically fit... :)
Locks aren't as easy to smash in real life as you might think, unless it was a lousy lock to begin with.