My Dad died 30 years ago and he had a couple smaller boxes like that he was starting to fill back up because the majority of his tools had been stolen from his truck. I kept the tools, but having just moved into a small apartment, I "thought" I didn't have room for them. I sold them to a good friend of his with the promise that if he got rid of them, I could buy them back. He moved unexpectedly and they were gone. Sure they were cheap boxes, but it would have been nice to have them. I still have most of the tools I got from him, but it would be nice to have the boxes also.
My vote is to hang on to them, and as others have said, store hardware, overflow tools in them. If you aren't into tools, or boxes, give them to a family member who is, or maybe a younger person in neighborhood who is into stuff like that, and get him to work on your lawn equipment as part of trade. You both get something from the deal, and your Dad's stuff is still close.
If you are like most here on the forums, there is NEVER enough tool storage.......ever.