A large part of the reason was that the geopolitical context of the 1980s was much friendlier to China than a century prior.

In the mid-late 1800s China repeatedly had to confront foreign incursions and wars from multiple different powers. Each time it lost it had to pay indemnities and grant both additional territorial and economic concessions to western powers which weakened its capacity to further modernize.

One example of this is that western powers forced the Qing to have very low tariffs, which in turn meant that domestic infant industries cannot be protected from foreign competition and thus much more likely to fail. At the same time western businesses gained preferential treatment in China as the result of the unequal treaties, they able to ignore Chinese taxation and laws and thus gaining an advantage over domestic enterprises which are subjected to taxation. The fact western business weren't subjected to Chinese courts meant that often Chinese cannot seek redressment for fraud, theft etc against those businesses because British/French courts are unlikely to rule against their citizens.

The indemnities themselves were heavy and because tariffs were capped at 5% by the unequal treaties (tariffs were a primary source of income for all countries during this time period), the Qing government was forced to take loans to pay them. The condition for those loans often included further economic concessions such as rights to build railroads, ownership of China-based assets and other preferential treatments. All of this meant that "defensive modernization" of the Qing faced fundamental barriers imposed upon it by foreign powers.

The PRC of the 1980s had an tactiful alliance with the US and the state was strong enough to deter foreign attacks. The Qing of the late 1800s was a semi-sovereign state, whereas the PRC was a fully sovereign one which could implement whichever economic policies it chose to. At the same time, the international situation arguably helped rather than hindered China. It had access to foreign capital through overseas Chinese communities which invested in the country, it had the developmental models of Singapore, Hong Kong and South Korea to follow. It had access to foreign markets to export to and it had cooperation with other countries which genuinely thought that China should be incorporated into the world market on equal terms.

This is not to say there's a whole host of difference domestically between the PRC and the Qing. There are a whole host of other reasons why the PRC succeeded and they have to do with the legacy of Laissez-Faire governance in the mid-Qing dynasty. but external differences and the geopolitical context is one of the key reasons behind why modernization failed in one but not the other.