How did the military strength of the northern and southern kingdoms compare later in history?

Initially the northern kingdom fielded 800,000 troops against the southern kingdom's 400,000. Later in history, the northern kingdom could only muster 580,000 while the southern kingdom brought 1,160,000, reversing the earlier advantage. This shift resulted from a mass migration of Israelites from the northern to the southern kingdom.

In 2 Chronicles chapter 13, Abijah of the southern kingdom of Judah and Benjamin could raise only 400,000 chosen men, while Jeroboam, the first king of the northern kingdom, set 800,000 men of war against him. That matched the reality of ten tribes in the north versus two in the south. But as Les teaches, following the numbers through later history shows the northern kingdom could eventually put only 580,000 troops in the field, whereas the southern kingdom came with 1,160,000. Les explains that a mass migration of Israelites out of the northern kingdom down into the southern kingdom over the years completely turned the tables.

2 Chronicles 13:3

And Abijah set the battle in array with an army of valiant men of war, even four hundred thousand chosen men: Jeroboam also set the battle in array against him with eight hundred thousand chosen men, being mighty men of valour.

Why was Jeroboam able to field twice as many soldiers as Abijah?

Jeroboam fielded 800,000 soldiers because the northern kingdom consisted of ten Israelite tribes, whereas Abijah's southern kingdom of Judah and Benjamin had only two tribes. That numerical advantage in tribes and population allowed the north to raise twice the troops.