The LCS-F (Freedom class LCS, the Indepedence class LCS is a very different animal so I think it is important to differentiate between them) has 2.5x as many RAM missiles as the 056, so I think that should be pointed out as its quite a big difference.
However, I think the main differences between the two are the result of the roles they were designed for.
The LCS-F is meant as largely an offensive ship, whereas the 056 is one designed for defensive missions. The two are also designed to hunt very different prey, which affected their choice of primary armaments.
I would expect the LCS-F to have much more range compared to the 056 since it will need to transit half way around the world to get from home base to it's intended area of operation whereas the 056 Only have to cover a short hop in comparison.
Since the LCS-F is intended to be able to deploy independently to pretty much any coast on earth, they would have been designed to be ocean going, and I would expect the LCS-F to have much better at weathering rougher seas compared to the 056.
I think that is where much of the difference in size between the two classes comes from. The USN required a ship with much more ferry range and high sea-keeping capabilities, which pretty much required a much bigger ship than the 056, and also a dedicated hanger.
I would also expect the LCS-F to be able to better at independent operations. Both ship classes are designed to operate with air defense and sensor support from larger friendly warships and/or airborne assets, however, I think the LCS-F would still be able to use all of its weapons to full effect without any 3rd party support, whereas the 056 clear would not be able to use its C802s at anything like full effective range without off-board targeting.
As a consequence of this, I think the LCS-F will have better sensors and battle management systems compared to the 056(which would help to account for the smaller crew size on the 056). The LCS-F should also be more individually flexible because of the mission model design.
The 056 is a bare bones general purpose patrol corvette (they might develop different variants for more specialised missions like ASW at a later date), it was designed to be cheap to build and operate in large numbers close to home. The LCS-F is a power projection ship built on the cheap. They might be largely similar, but they have very different missions in mind when they were designed.
