The only comparisons I can draw between the two is that they're open world and intensely focused on evoking a sense of adventure into wilderness and unknown. The expression of this vision; world building, game system design and implementation, questing, narrative, progression and pacing, puzzling, and so forth - all differs so significantly I could never see myself recommending one in replacement of the other. The end user experience and the facets it leverages as strengths, and deficiencies where the vision shows cracks, differ so wildly (PUN INTENDED) that I'd need to know what a person wants exactly from a game before I could recommend one over the other.
I personally prefer The Witcher 3, mainly because its strengths are immensely valued by my subjective experience and it resonated with me in a way I hadn't felt about a video game for a long, long time. Witcher 3 alarmingly dredged up desires I'd attribute to my dream game, something I never expected. That and I almost always disagree with the negative commentary reflecting the game design, particularly the combat, control, and exploration. The notion that The Witcher 3 is just story is such nonsense to me; it's not just story, and dismissing the value and weight of narrative and how deeply entwined into all facets of the game as just story is such a short sighted, simpleton view of the vision.
That being said, Breath of the Wild is a remarkable accomplishment for evoking similar desires as the Witcher 3, namely the freeform exploration and true sense of wonder. Breath of the Wild makes incredible strides in areas The Witcher 3 does not, but it's also not trying to be The Witcher 3. If I could draw one comparison between the two and where I felt one edges out the other, I would say the sense of reward for exploration in The Witcher 3 was more satisfying to me than Breath of the Wild. Funnily enough it's not because they both structure and reward exploration in the same way; they absolutely do not. But that I found myself more intrigued and rewarded consistently by The Witcher 3's unbelievable hand crafted visual and narrative detail in the world and questing, no matter how minor and insignificant, and what this meant for the world building as a whole, than scaling large stretches of terrain in Breath of the Wild where on too many occasions all was uncovered was a short (yet still enjoyable) shrine.
These discoveries in Breath of the Wild still felt rewarding and very enjoyable for their own reasons, but the repetition set in quicker. Even though it's just narrative or just graphics, in most cases even the simplest of Witcher 3 discoveries added something to the adventure as a whole; the shifting topography accurately marking signs of war and battles in an ongoing and very relevant conflict, or a just note in a treasure chest implying tragedy of drowned lovers and finding their bodies and wreckage in the vicinity. While Breath of the Wild routinely rewarded with fragmented pockets of isolated gameplay challenges, Wild Hunt eloquently wove even the tiniest details of narrative and lore into the greater whole. And if you were as invested in the lore, world building, and presence of everything within this fantasy universe as I was, these micro details being so seamlessly entwined into the greater tapestry of the adventure as a whole felt incredibly rewarding to uncover.
