With the recent induction of 056, a lot of comparison has been made between 056 and LCS. The comparisons are understandable. Both are just entering services. Both are expected to be built in large numbers and are also considered to be the lower end ships of their respective navy. In many ways, their comparison stops there, because Type 054A would be more comparable to LCS just based on the size and dimensions of the ships. I want to break this down to two sections: the differences in capabilities/cost between the two classes of ships and what that tells us about the two navies.
First of all, despite both ships are designed for littoral operations, one is designed to operate in its own waters, whereas the other is designed to operate in enemy waters. 056 is supposed to replace 053 and 037 in the role of patrolling coastal waters. It's equipped with enough strike power to conduct ASuW against other regional navy. With some modification, it can also be useful in ASW operations in the littoral waters. On the other hand, LCS is suppose to be faster, stealthier, far more modular and capable of operation in other country's littoral waters. USN has no need for something like 056, since it faces no foreign naval threat within its coastal waters. For any issues like smuggling, piracy and drug trafficking, it should be up to coastal guard to protect. At the same time, China has no need for a littoral ship as large or fast as LCS, because it really has no need in the near future for a ship built specifically to fight in the littoral waters of a non-neighbouring country. While most of the mission packages for LCS have yet to finish development, LCS will be capable of ASuW, ASW, MCM and special ops once that does happen. You might see more dedicated ASW or ASuW variants of Type 056 coming out, but each ship is really not expected to be doing more than one task.
As a result of this difference in roles and size of the ship, there is also a large gap in the cost of the ship. Each LCS cost over $400 million to build and equip. That's about twice as much as the cost of a Type 054A. Type 056 is expected to be a much cheaper ship than Type 054A, since it's much smaller. My current estimate for Type 056 is around around 60 million just based on the cost of Type 022, Type 054 and equivalent sized cutters (which run for about $15 to 20 million each). The relatively low cost of this should explain why China is able to build so many units in such short time while also build numerous other classes at the same time. If this cost more, China would not be able to use it to replace all of the old Type 053 and 037 ships. Despite the recent austerity in USN and the higher cost of American shipbuilding, USN still has a far higher budget than PLAN, so it could afford more expensive ships.
The size of crews also show us interesting things about the two navies. I think the crew size for LCS is supposed to be at most 75, whereas the much smaller 056 is expected to have 60 to 70 crews (even that is a reduction to 1/3 of Type 053). Even though Type 056 is far more complex and automated than the ships it is replacing, it's probably safe to say that it still lags modern Western ships. I think a large part of that has to do with the greater number of service personnels at the disposal of PLAN. Even with the rising labour cost in China, I think it's safe to assume that the compensation for a USN sailor is far higher than that of a PLAN sailor. Another part to look at is the huge leap facing sailors who are accustomed to operating a low tech ship like type 037 (I was told no training is required to be on that ship) to type 056. It's simply unrealistic to expect someone who has operated on Type 037/053 for their entire life to be able to be competent on something like LCS. As PLAN continues modernization, this expected improvement in software is often overlooked when one looks at the new ships that are coming out. The cost of training crew members will also go up as ships become more and more complicated.
Another interesting thing is the choice that the two navies made in developing these two ships. LCS is a ship expected to be modular enough to be able to easily reconfigure for different roles by changing to different mission packages. I expect different variants of Type 056 to come with each variant built with specific role in mind. Similary to Type 037, I would expect to see a Type 056 emphasize more toward ASW and one more emphasized toward patrol and another more emphasized toward ASuW. At the same time, LCS had the requirements to be able to travel at faster than 40 knots and also be extremely stealthy. It certainly pushes the technological envelope, whereas Type 056 does not. LCS is not only a new ship design but also requires new weapon system. Whereas PLAN rarely builds a shipping class that requires leap in both the ship design and its weapon system. I think this shows the background of both navies. USN always had a lot of money to spend, so it is willing to press for that additional performance on the newest ships in the face of budget overruns and delays. In comparison, PLAN had very little money back in the days and most of its programs was canned in the 80s and 90s due to lack of funding. So as a result of this, it has always been more conservative in incorporating improvement from one shipping class to the next. Compared to USN, PLAN is more frugal in the development of new ships and the management of its existing fleet. As an example, Type 052 underwent modernization recently, but the old HH-7 SAM was kept around instead of being replaced by more advance HQ-10 SAM. PLAN has a large stock of HH-7 missiles in stock and did not want them to go to waste by removing them from the ships undergoing modernization. It will be interesting to see how the perspectives of the two navies change in the future as PLAN continues to get more funding whereas USN starts to face austerity.