That would depend greatly on if you are assessing averages or the best of the best within each category, and what is considered police in the ancient world or modern world.
Ancient policing forces were not always independent of the states armies. If we for example look at the societies of central and eastern Europe, we would not find a dedicated police force. The tribes best warriors meted out justice both on the field of battle and in civil disagreements. If we take the more civilized states, like Rome, Greece, or Carthage one would find a different story, to a degree.
We have the most data about the Romans, and the effectiveness of their policing force. The early policing force, the night watchmen, were little more than slaves that had been assigned to carry buckets to any part of the city that was set on fire. They were replaced by the Vigiles, who were a more professional force. There was also the secret police, the Praetorian Guard. The Praetorian Guard were the emperors bodyguard and an elite military force in their own right, but they would have been the only force capable of policing larger sections of the empire.
In comparison, police officers of the western world are much more evenly trained for specific tasks. Traffic cops don't get the same training as a SWAT officer, or even an FBI agent. Even so, the more specialized units of western police forces are not typically comparable to the nations armed forces, nor are they necessarily trained for hand to hand combat in the same manner as necessary for an ancient warrior.
Even if you drop the equipment, the training and nutrition available to modern police officers is supplemented by modern knowledge. By and large, if you take the best combat modern police officer and face him off against the best combat ancient police officer, the modern officer should come out on top due to better preparation and training of a given individual that could choose to do so. If you take the average police officer and pit him against the average ancient police officer, the ancient officer should win, due to the preparation and training necessary to hold that position, compared to what is necessary for today's officers.