I highly recommend that you keep it in the factory boxes. That way, if there is a recall, or if you determine that some of it is faulty, or unsuitable for use (for whatever reason) in one of your firearms, you can easily segregate the affected rounds from the rest of your supply.
Also, if something happens to you, this will allow the unfortunate person left to deal with your belongings to positively identify the ammunition.
You can store the ammunition in the factory boxes in another container to help keep it compact, to protect it and to make it easier to move around.
The only way I would advise consolidating ammunition into different containers outside of the factory boxes would be if you keep it separated by brand/load and factory lot. Retain at least one of the factory boxes to provide the information that would help positively identify the ammunition in that container. You can remove the ammo carrier inside the factory box and flatten the box to save space .