Which dynasty had the best heavy cavalry?

In terms of real heavy cavalry, I would say Northern Wei.  The Northern Wei army used cataphracts- fully armored cavalryman and horse - in its divisions. 

The Han and Tang Dynasty armies were the most formidable in terms of cavalry warfare, but neither were particuarly noted for heavy cavalry.  Instead, both relied more on light cavalry.  The objective of cavalry warfare is speed, speed, and more speed.  The use of heavy cavalry would be significantly counterproductive to the purpose of cavalry warfare.

Here is a brief synopsis of the cavalry in various dynasties:

The Qin Dynasty.  The Qin army was infantry based, with cavalry as auxillaries.  The primary function of the Qin cavalryman was to serve as a mounted crossbowman.  Each Qin cavalryman carried a crossbow, and did not engage in hand to hand combat with the enemy.  A prime example of Qin cavalry warfare would be during the Battle of ChangPing, between the state of Qin and the state of Chao, where the Qin cavalry pelted the Chao army with missles from its mounted crossbowmen.

The Han Dynasty.  The Han army was the first Ancient Chinese army that truely embraced cavalry warfare to its maximum.  Due to constant incurisons by the Xiongnu/Huns in the North, the Emperor Wudi realized that, to defeat the Xiongnu, a formidable and mobile cavalry force must be trained.  Throughout the reign of Wudi, the Han army grew and so did its cavalry.  The Han cavalry did not have cataphracts, and primarily relied on speed and mobility.  Unlike their Roman counterparts, Han cavalrymen did not wear metal helmets, and wore fairly little armor.  Han cavalry was geared towards warfare with nomadic groups, and speed was essence.  The defeat of the Xiongnu by generals Wei Qing and Huo Qubing, and the subsequent expansion of the Han Empire into Central Asia, could not have been realized without its extremely mobile cavalry force.

Han Cavalryman, notice that he does not wear a full metal helmet.

Post Han and Pre Tang Period.  The most prominent cavalry after the Han Dynasty belonged to that of the Northern Wei, whose rulers were Xianbei, a Northern nomadic group that eventually assimilated with the Han Chinese.  The Northern Wei cavalry utilized cataphracts, where both the cavalryman and the horse were fully armored.  I would say that out of all dynasties, the Northern Wei had the heaviest cavalry, on average.

The figure to the right is mostly likely a Northern Wei Cavalryman.  Notice the fully armored cataphract.

The Tang Dynasty.  Tang Dynasty cavalry served a similiar purpose to that of the Han Dynasty cavalry - to win against nomads and expand into Central Asia.  This time, the nomadic enemy were the Gok Turks.  The Tang cavalry was successful in defeating the Gok Turks, and in helping the empire to establish a strong presence along the Silk Road.  Like the Han Dynasty cavalry, Tang Dynasty cavalry was relatively mobile, and unlike contemporary Byzantine and Tubo cavalry, the Tang cavalry did not use cataphracts.  The Tang cavalryman generally wore a full suit of scaled armor, from head to toe, but the horse was unarmored.  After the Anlushan Rebellion in the 750s, the Tang Empire lost its strongholds in its western borders, and consequently, lost its source of horses.  Its cavalry declined and its borders shrunk.

Tang Cavalry.  Notice that the horse is not armored.

The Song Dynasty.  Unlike its neighbors (Khitans, Tanguts, Jurchens, and Mongols), the Song did not have a fully competent cavalry force, because it lacked sources for horses.  Instead, the Song concentrated on heavy infantry, and advanced rocketry.  Horses within the Song army were reserved for officers, and usually one can only spot one horse among a horde of infantry.  The lack of a fully independent cavalry force proved to be devastating to the Song in its wars against the Khitans, Tanguts, Jurchens, and Mongols.

The Yuan Dynasty.  Mongol cavalrymen, mongol tactics.

The Ming Dynasty.  The early Ming Dynasty cavalry relied on Mongol tactics, and because of constant warfare with Mongols, resembled the Mongol cavalry forces.  Later in the Ming Dynasty, the military became increasingly weak and corrupt, and a new cavalry had to be invented, by an ingenious general named Qi Jiguang.  Qi Jiguang intergrated wagons and firearms into cavalry warfare.  The basic tactic is as follows: A circular wall of wagons surround and protect a division of cavalrymen.  Inside the wagons are posted infantry armed with guns.  When the enemy cavalry approaches, the wall of wagons close into a circle, and the gunners pelt the enemy with firearms, so that the enemy cannot get close.  After weakening the enemy cavalry with firearms, the circular wall of wagons would open, and the cavalrymen behind the wagons would charge forward to finish off the remaining enemy forces.  It was reported that, after hearing of the innovative new cavalry tactics invented by Qi Jiguang, the Mongol Khan voluntarily seeked peace with the Ming.

The Qing Dynasty.  The early Qing military used cavalry as one of its primary strengths, and as the pride of the Manchu bannermen.  Yet, as firearms gradually reduced cavalry warfare into secondary status, the Qing cavalry lost its advantage.  Later Qing armies, such as Zeng Guofan's Xiang Army and Li Hongzhang's Huai Army, were almost entirely infantry based, and armed with imported firearms and cannons.

Sidenote: These are my notes, and have nothing to do with Wikipedia.