There are several consequences of the differences between the US (and the west) and China (and other autocracies). First, with one of the major assumptions of neoclassical economics out the window, it calls into question basing economic policy on neoclassical economics. Second, with a monopoly structure for intellectual property several different economic incentives have been created. Finally, the differences in IP management between the countries creates tensions at several different levels. I'll discuss each of these points in more detail.
First, if one of the major assumptions for economic policy includes non-rival, non-exclusive knowledge, it's difficult to understand why there isn't more competition in many markets. However, as we know it's not really possible for any firm to pick up any sort of technology and start to produce a given product. Because of this difficulty regions and areas tend to become experts at specific types of technologies. However, even in the case of China the freedom of access to IP makes it easier for firms to produce specific products. The problem still lies in the fact that you still need tacit knowledge to actually make the product. A patent is supposed to give you the information you need to produce the technology. However, the actual patents are difficult to read and not likely to be possible
Second, with a monopoly structure in place for intellectual property it gives very different incentives for owners of intellectual property. First, for people who actually produce a product, attacking products that are similar for infringement can be a very lucrative proposition. It prevents other companies from becoming competition. Apple is currently using this tactic to go after Android through Samsung and HTC. With a full monopoly technological progress can actually come to a standstill. An example of this is with Xerox copiers. With the monopoly in place Xerox did not innovate and kept prices extremely high. As soon as their patent ran out the competition came in and almost took all of the market share from Xerox. They introduced lower priced products and a wider more personal product range. Without the monopoly in place other companies could try to move into the market space earlier and drive innovation from the beginning of the market. Finally, with reduced ownership of IP there will be less patent trolls like Intellectual Ventures.
Third, the IP management is causing issues between firms and the Chinese government. The firms do not want to give up their IP because it's how they are able to make their money. Some of these technologies are so easy to copy it's impossible to make a profit without protection. In theory pharmaceuticals should be perfectly copyable based on the chemical properties of the drug. If the pharmaceutical companies didn't have a chance to recoup the investment on a drug (500 million - 1 billion per drug) there would be no innovation. The differences present problems for trade and agreements between countries. The US and China have had serious disagreements over how IP should be managed.
Basically, the differences in how IP is understood impacts a countries policies economically and in trade. It is important to understand exactly what's going on with these issues. Our governments are pushing for different levels of control over IP both in patents and other forms of copyright. As some one interested in policy, it's important to understand what types of policies we should be pushing for. I don't think there's any true right answer for the IP problem. In different situations policies should be adjusted. We cannot have a stagnant IP regime when technologies are evolving as fast as they are.