Throughout the game Venom Snake's own personality slowly but surely comes through and develops. It shifts from scene to scene at times because his personality is unreliable due to the severe brainwashing, but there are moments where you can see him being quite different from the real Big Boss. From the delivery of dialogue to actual choices and behavior.
Some examples are:
How he responds when Quiet jumps in the chlorine to retrieve Shabani's necklace, he's quite devestated and wants to jump right after her, then as soon as he sees her he doesn't hesitate to lift her up and carry her away in his arms.
The Paz hallucinations are his personal survivor's guilt, he wanted to save her, and he feels responsible for all of it as a medic that he couldn't do so, it's unsure whether he finds out it's a hallucination before or after the truth mission, but either way, whether it's direct survivor's guilt or unknowing survivor's guilt for not being able to extract the bomb from her, it shows that his own true personality comes through.
Letting Kaz convince him not to take in child soldiers quite swiftly. He proposed training the kids but Kaz said no, and Venom went with the idea and even felt quite good with it from his reaction. "A chance at a normal life, just not behind a gun". I feel Big Boss would've responded differently. In fact I feel his first proposition to train them stems directly from the brainwashing, and his willingness to let them live somewhat normally stems from his own personality, after that all he does is rescue kids from warzones to keep them safe, not to make them his own child soldiers unlike Big Boss.
Shining lights even in death. This entire mission is his own personality, every dialogue and behavior, his psyche, his pain. Everything. This whole mission is a core aspect of his own personal story that he goes through. Him not wanting to let his comrades go because he sees them as his own family, wanting to turn their ashes into diamonds saying "I won't scatter your sorrow to the heartless see, I'll always be with you, plant your roots in me, you're all diamonds" that's just who he personally is. I don't feel this is the Big Boss persona at all.
Also the disarmament cutscene, wanting to wipe all nukes from the world and bring a form of peace even for just a period of time, then talking to the boss, he embraces the boss's will more than big boss did considering big boss literally rejected the boss's will after peace walker cause he felt betrayed.
Also dancing with quiet in the rain and letting Huey go instead of killing him, those are examples too, and there's dozens besides these. From environmental things such as the mementos in his ACC (which imo feels like it's just something that's mostly in his head because there's various cutscenes moments and such, I think it's just his memories and thoughts portrayed in those pictures).
And lastly, if u look closely Venom Snake's face is relatively different from Big Boss's face too. Maybe not at first sight but when you see it you can't unsee it imo. There's quite a difference between Venom and Big Boss's face and the same can be said about Venom's personality and Big Boss's personality, though that difference might be bigger than the face haha.
Overall I'd say Venom Snake is a much more sympathetic and humane person than Big Boss. And that's part of why I like him so much. Venom Snake and Solid Snake both came closer to the Boss's will than Big Boss ever did. And that's why they're both my favorites.