I think the difference between Solid Snake and Big Boss is that Big Boss got a game where we could play him as a rookie and see him turn into a legend as the game goes on which is where a lot of people may prefer Big Boss.
However, I am of the opinion that having more development doesn't necessarily make you a more interesting character. I still find Solid Snake, at least during his prime in MGS1 and 2 more interesting because he always had interesting things to say. He was experienced, knowledgeable, and held a lot of self-respect to the point of humility. If I can throw some real talk, for all of his obsession over The Boss, Naked wasn't able to say the kind of beautiful things Solid was able to for Sniper Wolf out of massive respect and honor.
I notice that most of the Snakes in the Snake family are failures in some way. Big Boss became a massive villain, and Solidus and Liquid tried to follow his steps (in different ways), ultimately failing as well... so how does Solid Snake manage to overcome such a curse? I think it's simple: he was the only one that grew as a soldier in such a way that would make The Boss proud, while at the same time walking a path that was his own and not hers. For this reason I consider Gray Fox secretly the most important character in the MGS series, even more than The Boss herself for influencing Snake positively with a single line: "We aren't tools of the government, or anyone else. I at least always fought for what I believed in."