I don't think it is as simple as saying one holds the power and the other doesn't. I believe it is more... collaborative than that.
Obviously the sub has power in the respect that at any time they can end the activity/exchange/scene/session with a safeword. Their submission to the dom is voluntary and as such they hold that power at all times. They also can set boundaries, limits, and rules for a scene with their dom beforehand that sets the scope of what will happen within it. In some ways the sub controls the fundamental aspects of what happens in a room before ever stepping into it. They also can control, to some degree, the outcomes of any actions taken during a scene by how they react during the scene. If they react positively (which, to be clear, does not necessarily mean 'joyfully') then the dom will be incentivized to take further actions in a certain direction, while if they react negatively (again, this can mean different things to different people; e.g. boredom as a negative reaction vs. crying out in pain as a positive one) they will be deincentivized from taking certain actions and may switch to something else. In many ways the sub and their desires are the prime focus of a scene.
Obviously the dom has power in the respect that they control the actions and behaviours of both the sub and themselves. In a most objective-level view the dom controls the actions of the scene and their desire is manifested in a literal way as they give the sub commands which the sub obeys (or fails to obey, leading to consequences the dom controls), performs actions upon which the sub has 'no' say (note: see limits/safeword discussed above), and decides upon the direction of a scene. While they often do (and arguably should) use the sub's reactions to guide their decision-making they are not, strictly speaking, bound to. Meanwhile the sub is often both figuratively and literally bound at the will of the dom's decisions. Furthermore, although it is not often discussed, the dom may use a safeword as well and can set limits just as a sub can in order to control what happens before a scene begins. If the sub is the stage, the dom is the director.
However a scene is not just two agents (dom and sub) acting individually, they are two people who are acting together and actively responding to the other. There is communication happening during a scene, although it may not necessarily be verbal. The actions the dom takes and the commands they give to the sub hold meanings that the sub will pick up on, even subconsciously, and the sub will change their behaviour in response. The way they respond gives the dom information which they use to change their own behaviour, and this flows back and forth between the dom and sub in a 'conversation' of sorts. They both together control different aspects of the greater whole between them and together they create something that doesn't exist without both of them working together.
So, in summary, both the dom and the sub have power over the scene.
