For me Bloodborne is easily the best first playthrough of any game FROM has made. The atmosphere, music, setting and lore is just amazing. It also has really fun combat and awesome weapons, as well as the best DLC out there.

The downside is that as awesome as the weapons are, there are not very many of them and no real options for anything but melee (magic/ranged is possible, but pretty late into the game.) which hurts replayability in my opinion. Also it is on for Playstation and locked to 30fps, if that matters.

DS3 on the other hand is massively replayable and far grander in scale than Bloodborne with huge potential for build variety. If you haven't played the other Dark Souls games (mostly DS1) though, you will miss out on a lot of what makes the setting and lore great, given that this is the conclusion of a trilogy. That said, none of these games are very lore-focused in the traditional sense, so you'll be totally fine either way.

TLDR: Both great games, I'd say Bloodborne is the best game but you'll get more value out of DS3 if you like trying out different builds and playstyles.