You are asking a question that goes to the heart of electrical design. DCP is correct in the information provided in the two post.
Low voltage power circuit breakers (LVPCB) are the older workhorse of the industry. They are fixed or drawout mounting, have an interrupting rating and a withstand rating that were missing from olded molded case circuit breakers (MCCB)and were generally preferred for industrial and large commercial applications because their trip times were adjustible to allow coordination with upstream and down stream devices.
In todays market MCCBs with electronic trips do cover most of the coordination problems, but most still need an instantenous trip even if a short time delay is included. MCCBs can also be purchased with higher interrupting ratings without added fuses for the higher ratings to a point.
Insulated case breakers are similiar to the MCCB except with more withstand ability and a higher price.
To answer your question maintenance is the question. A drawout LVPCB is easier to maintain and clean and test to assure operation within initial settings. MCCBs are typically fixed mounted and are therefore harder to test trip without removing the entire switchboard from service and removing the circuit breaker from its mounting. This seldom happens.
Newer electronic trip devices on all three classes of breakers allow trip device testig with a low current and low voltage testset to verify the settings in lieu of the high current testset required for testing at full current.
A rating of 800 amps with an AIC of 25,000 amps set for 630 amps is within the ability of most MCCBs until you get to 600 volts. You did not state voltage and to get 25,000 AIC at 600 volts requires a high interrupting capacity breaker.
I would not recomment a fixed trip MCCB for a main application because of the limited coordination with down stream devices which would have to be rated about 50% of the main trip rating. Also with a fixed trip device you will have to choose 600 amps or 700 amps to come closer to the stated 630 amps.
If either type MCCB is selected it should be operated at 80% of its continuous current application. An 800 amp frame breaker is required for a continuous 630 amp load. With the LVPCB it can be operated at 100% load, but at the 630 amp level it becomes a mute point.
All the information provided herein and that provided by DP assumes a low voltage system, 600 volts or below. This information was not provided in the original post.
I am not aware of any standard for the application of one type vs. the other. Aorrect application of either is approved by UL and the NEC. The preferred application is a question of maintenance preference, downtime cost affect and length of life vs. initial cost.
Hopes this helps.