from what I've seen, no. They are not 'subsets' of each other if you like, if you use handbrake with a very high quality factor you'll not lose anything, but it will probably be larger than the original.
I tinkered a bit with several different media types and here is what I have concluded.
Converting h.264 to h.265 is no big deal with animation. It is much harder with live action as you are adding more compression on top of the existing compression. On average, I was able to get a 30% reduction in file size with an animated feature, avoiding pixelation. Live action files were larger than before.
It would be worth it if your file is abnormally large, say 4+ gigs for a 1080p movie at 2 hours on h.264 compression.
personally i'm looking at full BR rips of my BR's so 20-30GB, where there might be some benefit, But processing time vs simply buying another disk... i'd just get another disk or two. However being able to run it over wifi would be a benefit.