Let say we have the worst case scenario where a bunch of criminals successfully enter the capital building and occupy it. Is the best response to send the army, or as many police units as needed to apprehend the criminals and put them in jail?

By sending the army what we are saying is that there existed a creditable scenario that the people attacking could have taken control of the US government and ruled over the nation.

The National Guard is not the Army, it's a dual-purpose force that is both a reserve for the Army and a reserve for civil authorities during emergencies including civil disorder.

> By sending the army what we are saying is that there existed a creditable scenario that the people attacking could have taken control of the US government and ruled over the nation.

No, even if we were talking about the Army proper, an existential threat to the government is not the criteria under the Insurrection Act for their use to disperse insurgents.

The militia, armed forces, or both may be used (among other scenarios authorized in law) against “any insurrection, domestic violence, unlawful combination, or conspiracy” which “opposes or obstructs the execution of the laws of the United States or impedes the course of justice under those laws”. 10 USC Sec 253.

History is full of examples and dead bodies where the military has been used against its own people who oppose or obstruct the execution of law. It many countries it also follows a period of regret and new laws in order to prevent something similar to ever happen again. Just because the government has a law that gives them authorization to send the military in order to secure a building, it doesn't mean it is a good idea.

Would the military trained personnel have done a better job during the capital attack than the police trained one?

The Guard is a force whose missions include support for Civil authorities during disturbances, and it's training, equipment, organizations, planning, etc. reflect that.

And, quite arguably, that are better than, and trained better than the police for, dealing with large scale civil unrest.

https://apnews.com/article/election-2020-elections-racial-in...

https://www.ideastream.org/news/what-national-guard-training...

The fact that you have to reach back that far, given all the more recent problems with conventional police, seems to illustrate my point.