This is a walk-through (Notice !)
These two dynasties were often compared for their similarities, so this answer is somewhat directed at their differences.
As you go through, you would realize that many of these were in fact closely or loosely related to the political philosophy of Tang.
Imperial examination
This procedure of formal selection proceeded through various stages. A "nomination and inspection system" was imposed by the Han Dynasty. It required local leaders to recommend respectable persons for government jobs. This worked "when it worked," but it failed because the structure allowed for nepotism and cronyism. Nominees frequently lacked the necessary skills for the role. The Sui Dynasty proposed the Imperial Examination. It was greatly enlarged upon during the Tang Dynasty. It assessed the examinees' knowledge and talents, regardless of their family rank or connections. Li Shimin, Emperor Taizong, famously declared, "All talented individuals in the world are now within my reach."
Future Emperors and Dynasties proceeded to strengthen the system, including redaction of the examinee's identity during grading, an imperial interview with the Emperor himself at the end, and extremely harsh penalty for cheating examiners and examinees. It was not only an efficient method for selecting officials, but it also stressed the importance of education. As a result, throughout the following thousand years (and until now! ), "best test score" was part of "the Great Chinese Dream." In literature, it was a typical rags-to-riches story technique.
Restricting the power of prominent clans
In the Han Dynasty, many clans eventually became very powerful. Notice how in Three Kingdoms, Yuan Shao and Yuan Shu always bragged about their clan? The Sima family was also a powerful clan and this trait persisted in their Jin Dynasty, and even the Southern-Northern Dynasty.
In a period of civil conflict, even Emperors had to seek help from local clans. At best, powerful clans may influence government decisions; at worst, they could amass enormous regional control. The governing class was also descended from prominent clans, such as the Yuwen (Xianbei Zhou Dynasty), Yang (Sui Dynasty), and Li clans. However, in order to avoid any threat to their rule, the Tang Dynasty suppressed localism to the greatest extent possible. Empress Wu Zetian despised it in particular, and her draconic authority diminished its power even further.
As I previously stated, one such option was the formation of a bureaucratic system tied to meritocracy. The Imperial Examination was used to choose local governors, magistrates, and administrators. Local clans with clout no longer propose candidates who are linked with them. This enabled the central authority to divide their region into provinces and administer power more efficiently.
During the Song Dynasty, most powerful clans were just "wealthy," not powerful. They've largely withdrawn from politics.
No regional prince-lords
During the early years of the Han Dynasty, numerous members of the Liu family held Lordships in various places. The Tang Dynasty, on the other hand, did not, presumably due to the familial rivalry that existed at the time of its establishment. Li Shimin was once considered to be given lordship of Luoyang as prince (which potentially could’ve split the newly found Tang into two), but his brother (crown prince) Li Jiancheng refused. And then the Xuanwu Gate incident happened where Li Shimin killed his brothers to eventually take the crown himself.
The promotion of various princes to Lords of various regions, as history had shown, was always a recipe for disaster. The Han Dynasty had the Seven Kingdom Rebellion, and the future Ming Dynasty had the civil war between Emperor Jianwen and Yongle. This again gave more power to the regional officials to have full control over their administrative region, but this policy also went to a new extreme after many generations to give rise to An Lushan (a story for another day). Warlord-ism became a significant threat that the Tang Dynasty never really could solve and eventually caused its downfall.