This may get a bit spoilery, but I'll do what I can to avoid them.
The things I see to be characteristic traits of the Cosy Cafe MC: he's a normal guy with no extra power or strength beyond a normal person, but he is strong-willed, dominant, stubborn, and has a passion for a particular desire/goal. He treats his women well but in a dominant fashion, and engages in discipline play regularly. He has true affection for his girls, and gets actively angry if they are threatened. He gets annoyed by people pushing at him, or forcing or manipulating him into doing things, and tends to act in a contrary fashion against those people, acting against them not because he agrees with their enemies, but because they tried to control him. He is cautious around the unpredictable or unfamiliar, and tries not to act until he has more information (which kinda screwed him a bit during the Hamilton party).
Of those, the only thing the Secret Island MC shares is that he's strong-willed. The Secret Island MC is not a normal guy: he is a sorcerer in a place where magic is rare and is also not human, having lived many times longer than humans or even elves do. He is stronger, more powerful, and more knowledgeable than almost any other individual he is likely to encounter in the game. He is calm and unflappable, and while he isn't particularly dominant and doesn't try to dominate anyone or play dominance or discipline games, he is non-submissive, and would never let anyone dominate him. If it came down to one or the other, he would dominate rather than be dominated, but it seems like he'd do that more out of necessity than out of any desire for dominance in general. He also doesn't really have a strong drive/goal beyond escaping the island. His feelings towards his girls don't really seem like true affection (they're instead described by someone who is probably the same species as the MC as being more like they're his pets who he's fond of, and not equals). He doesn't really get angry at anything; while he's working to protect the girls, even the ones not in a relationship with him, it's not out of anger, but out of prudence and protectiveness. He mostly passively resists manipulation, and even goes along with it if he agrees with its goals/purposes.
And, again I'll reiterate, it's a decent game. I've been enjoying it. It's just nothing like Cosy Cafe, and he's nothing like the Cosy Cafe MC beyond not being submissive.