How many fighting men were found in Judah and Israel?

2 Samuel 24:9 and 1 Chronicles 21:5

1. Five hundred thousand (2 Samuel 24:9) - "And Joab gave the number of the registration of the people to the king; and there were in Israel eight hundred thousand valiant men who drew the sword, and the men of Judah were five hundred thousand men."
2. Four hundred and seventy thousand (1 Chronicles 21:5) - "And Joab gave the number of the census of all the people to David. And all Israel were 1,100,000 men who drew the sword; and Judah was 470,000 men who drew the sword."

Regarding Israel's number difference:

The solution to the difference in counts for Israel seems to be answered in the Hebrew word for "valiant," which is "chayil" found in 2 Samuel 24:9. It means, "men of valor, army, host, etc." It seems to mean that the men numbered in 2 Samuel 24:9 were those with battle experience where the men of 1 Chronicles 21:5 were not. It was most probably true that there were an additional 300,000 men ready for battle who had not yet experienced it. Therefore, 2 Sam. 24:9 numbers only the experienced men, where 1 Chronicles 21:5 numbers all men of battle ready age.

Regarding Judah's number difference:

The solution seems to provided for us in the following verse, 1 Chronicles 21:6, which says, "But he did not number Levi and Benjamin among them, for the king’s command was abhorrent to Joab," (NASB). Verse six states that the numbering process had not yet been completed since the tribes of Levi and Benjamin had not been numbered.