Well, I would consider myself more in the "do not limit my available tools" as a DM camp. But you know what, even that's fine to a large degree. There are already limitations.
Most of the time, my input as far as rules are concerned during the game is minimal. I present the world, play the NPCs and monsters, etc. and we follow the rules.
I use passive skills extensively, so we don't have to roll skill checks frequently, but that's still skill vs DC. Although there are plenty of actions the players attempt that may not have a direct correlation in the rules. So I choose the most logical fit.
If the players go in a direction that's unexpected, I need to deal with that. It's based on a combination of rules, random tables, and improvisation.
But my goal is to influence the narrative as little as possible. My input into the narrative is through the NPCs and monsters. For everything else I'm just there to referee the world and setting.
So I don't know what you want to call it. The rules are good at mechanics. It also maintains consistency. I have goals and personalities for NPCs I expect them to meet, but if they go in a different direction I can work from tables, or do it on the fly. However it's most seamless for the players. If I roll it randomly then I have to see how, if at all, that ties into whatever else is going on.
So I'm not sure I would use the term Big DM. I'm here to provide the stage for the characters. The players write their characters' story.
Perhaps my approach is more about putting the focus on the characters, and letting the players have full control over their actions and decisions? I don't know, that sounds pretty DM Light to me. The DM interferes and controls as little as possible.
An adventure designed with a set plot and expected outcome as determined by the DM? That sounds more like Big DM to me. Many of the APs and certainly a lot of adventures from the past fit that approach. It seems like that approach is more about the characters playing the DM's story.
I don't want the focus on me, and it's not about my story. I do provide a framework, and you can say it's my world, but I'm most interested in seeing how the characters, as people, handle life in a dangerous and magical world. I'm more interested in what they can come up with than me.
That to me is far more interesting to me to see if they can successfully get from point A to point B efficiently in something I preplanned for them. I guess for me there is no point B.
And that's the thing, from my perspective, it's not about the DM at all. Really, I prefer for the DM and the rules to be as invisible as possible. I think both are essential, but neither are the focus of my game.
Big DM is not a derogatory term, I merely use it to refer to a DM who exercises a sizable influence on the progress of the game once it begins (in the form of content creation/modification and ad hoc rulings). DM Light refers to someone who tries to limit such in-game influence by front-loading his need for such influence in the key. That's the limit of what the terms represent - and btw I see them both as valid methods depending on what you like. The terms are based on the division of styles illuminated in the quote I began with.