Depends on the situation.
First, just to clarify, stopping power is actually a function of the tire. The tire's grip on the road is what stops the bike. A bike's maximum stopping power is reached when the tire is at the point of lockup. All brakes just allow you to modulate that power and maintain control, while dissipating the kinetic energy of the bike as heat. So in that regard, all brakes that can skid the tire have equal stopping power. Any advantages a brake has are in other areas.
Rim brakes are great at low speeds. essentially a rim is a giant disk. Since there is more surface area, they dissipate heat better and run cooler. their pads are optimized for cooler temps and so can use a thicker pad since heat retention wouldn't be an issue. they can also operate at a lower pressure since they have a higher mechanical advantage stopping the wheel near the tire instead of near the hub. Both of those factors means the pad will last longer.
Also because they operate so close to the tire, they have the highest degree of precision and offer the greatest potential for razor sharp modulation. There's a reason many stunt bikes use rim brakes, as they offer unparalleled precision.
Also in their favor, they are one of the lightest weight braking options. They also can be placed in the shadow of the frame, and are one of the most aerodynamic braking options. They also put no stress on the spokes, so a lighter weight wheel can be built.
They have downsides. If the rim isn't true, or if the rim gets damaged on a rock, bump, log, pothole, squirrel, or other road hazard, the effectiveness of the brake is reduced. That loss of effectiveness is exacerbated by high speeds. The faster you go, the more critical a perfectly straight smooth rim becomes. There is risk in running a rim brake at high speeds because any thing that effects the wheel can leave you with poor to no brakes.
They don't play well in the wet, and they do abysmally in the mud. Unfortunately rims are prone to get wet and muddy, especially off road.
Also, wind, water, snow, ice, mud, etc can change the temperature of the rim. that effects the way the brake pads interact with the rim and effects modulation consistency. The amount of hand pressure needed to stop the bike won't always be consistent.
In general, it takes more hand pressure to operate a rim brake than a disk brake. they take 2 or more fingers to use for most people
Disk brakes don't offer the same laser precise precision, but they come damn close. More like razor precision. They are up away from the wheel, so mostly immune to the mud and gunk on the road or trail. they also designed for self cleaning, so they are more tolerant of mud, snow, water, blood, guts, and the general whatever that gets splashed on them along the trail. Just about anything that could damage a wheel and still leave the bike mobile won't hurt the disk, so if the tire holds air, and the wheel can turn, it should be rideable.
Since the pads are designed to work at high heat, and are designed to generate their own heat up to a point, they are less effected by the environment. changes in environmental temperature are less of a percentage of their total temp so cause less change in performance. A mech brake like a BB7 takes 1 finger, a hydraulic brake can be operated by a butterfly fart.
Disk brakes take less hand pressure to use than rim brakes.
On the down side, Disk brakes eat expensive pads. they need a heavier hub and thicker spokes. While damage is rare as they are fairly protected, even a millimeter bend in a disk might put a bike out of service. They weigh more. They cause more aerodynamic drag. And they just aren't as precise.
As for maintenance, I think it's a wash. Rim brakes need perfect rims, that means a fanatical attention to keeping the wheel running true. But disk brakes need constant pad, cable, and/or fluid maintenance. As someone who rides both, I don't think either is better.