In the beginning of the game this feature is not important, but as you progress and start to upgrade your gear, or start to manufacture new gear it’s important to understand the difference between breaking an item and disassembly of the same item.
In short the difference is connected to either you want to build new gear and new items or if you need to enhance gear to give it better boost.
Build new gear
In manufacturing you need materials. You get materials by breaking an item. In addition you get spare parts.
The result is dependent on the quality of the item. In this case we broke and disassembled to same level 10 item as an example.
The pictures above shows we get an item or new materials. In addition we get Spare Parts.
This process require that you have access to the Combat lab.
In the Combat lab there is an option to enhance gear. If we disassemble the item instead of breaking it. The result gives us just spare parts. The difference is in the amount of Spare Items.
While we got about 1000 Spare Parts when we broke it, we get about 100.000 ie a hundred times as many Spare Parts when we disassembles the item.
As a conclusion you should break an item if you want to manufacture something, and you should disassemble the item if you need Spare Parts for enhancement of gear due to the different volumes of Spare Parts the disassemble process gives vs the break item process.