The universe created for Avatar: the Last Airbender and The Legend of Korra draws inspiration from real-life China, Japan, India, Korea and the Inuit peoples, and it also uses the four classical Greek elements. The magic system is bending, and earthbending dominates the second season of Avatar.
Two particular corps of earthbenders stand out in the franchise: the Dai Li, the elite secret police of Ba Sing Se, and the metalbender police force of Republic City. The benders in both organizations are skilled professionals, but when they are compared, which one proves superior? Let's break it down and find out.
The Dai Li
The Dai Li are the secret police force in Ba Sing Se, proving that the Fire Nation isn't alone in having insidious bender groups. Ba Sing Se is a closed-off and durable city, strong and secure like the Earth itself -- but not in a nice way. Eventually, Ba Sing Se stood alone against the Fire Nation, but the people inside didn't even know that there was a war on. The leader of the Dai Li, Long Feng, uses the facility under Lake Laogai to brainwash people and erase their memories in order to better control the city.
Enforcing Long Feng's will are the elite Dai Li, all of whom are earthbenders. They aren't showy like the earthbending fighters in the arena, they are more like ninjas -- using stealth and coordinated ambushes to take down their enemies with minimal resistance. How does blunt earthbending make this possible? For the most part, the Dai Li use compacted earth and rocks to form human hands, and fling these earth hands to grab a victim's wrists and ankles (or even cover their mouth). These rock hands are difficult to see or evade, and the Dai Li can drag anyone off with them.
That's not all, though. The Dai Li can use earthbending to stick to the rocky ceilings of various buildings, especially in the Laogai facility or Old Ba Sing Se. This gives them a cunning vantage point in battle and lends them some added stealth capabilities as well. If needs be, the Dai Li can lift larger chunks of rock and soil to use as blunt projectiles, as well as rapid-fire rocks to cover a wide area with suppressing fire (as seen in The Legend of Korra). They are never seen bending metal, but with their current skills and capabilities (not to mention their role), they hardly need to. On top of all that, they are highly disciplined, coordinated and precise, no matter the situation. It seems that nothing can cause them to hesitate, panic or retreat.
Republic City's Metalbender Police
By design, Republic City is a multi-national city, and firebenders, earthbenders and waterbenders all rub shoulders. As for policing this enormous city, this job falls to the metalbender police force. Founded by the legendary Toph Beifong, the first-ever metalbender, these police officers have been keeping the peace for decades.
This means that they are well-equipped for the job. Metalbender police officer uniforms include gray clothing and caps, not to mention armor plating on their chests and upper arms. This protects them from a variety of attacks, excepting bloodbending and lightning bending. To get around, these police officers have metal cables coiled up on their uniforms, and they can use them to swing around Spider-Man style. But this isn't just for mobility; the metalbender police can use them to capture criminals and escaping vehicles.
In addition, the police enjoy an entire fleet of cars, as well as zeppelins that patrol the skies. It is easy for metalbender police officers to leap out of those zeppelins with their cables and land on rooftops or the street, and they can get back into those zeppelins the same way. The police even captured Korra and her polar bear dog Naga with their cables while riding on a zeppelin, and carried Korra and her mount to the police station.
Which is more effective?
The Dai Li are the more effective corps of earthbenders. While the Republic City police officers have access to vehicles and can bend metal (while the Dai Li seemingly cannot), the Dai Li have a few distinct advantages. Primarily, their stealth. Despite being earthbenders, they are among the stealthiest warriors in the entire Avatar universe, being able to appear and disappear before anyone can react to them. They do this by operating at night and using their knowledge of Ba Sing Se's streets, and it is easy to presume that if they learn the streets of any other city, they could do the same thing anywhere. Their earthbender hands are an enormous asset, allowing them to quietly capture and subdue anyone and restrict their wrists and ankles, preventing resistance. That, and the Dai Li can easily stick to ceilings and act in perfect unison.
By contrast, the Republic City police are competent at their jobs, but they repeatedly lost to the Equalists, and their zeppelins are obvious targets. Their armor is effective against blunt attacks, but does nothing against lightningbending or bloodbending, while the Dai Li's stealth allows them to subdue someone before they can even attempt such attacks against them. In theory, the Dai Li can capture absolutely anyone without taking return fire, owing to their stealth and earthbending hands. The metalbender police fight in a more conventional manner and they can be beaten.