The description in Samuel is of 'the inspection of the people . . .800,000 men of valour, drawing sword.' [Young's Literal] or 'the mustering of the people . . . 800,000 mighty men, drawing sword.' [Green's Hebrew Interlinear].
In Chronicles it is 'all Israel - 1,100,000' [Young's Literal] and 'all Israel - 1,100,000'[Green].
In Samuel the word is chayil - 'valiants' [Young].
In Chronicles it is am - 'people' [Young].
It is clear that, with regard to Judah, the figure of 470,000 - quoted in Chronicles - is just those who drew sword, whereas the Samuel number is all of Judah, 500,000.
And it is clear that, with regard to Israel, also, a different thing is being measured, either all the people, in Chronicles, or merely the fighting force, in Samuel.
This difference, regarding Israel, is to be expected by Young's and Green's selective choice of wording 'mustering' and 'inspection', in Samuel, which have a military connotation suitable to the gathering of troops, rather than, in Chronicles, the gathering of the whole populace.
In Switzerland every man has a rifle at home, in a locked cupboard, and in time of war - if that ever happened in Switzerland - the whole male populace would turn out and fight. But as to the proficient, the proven valiant, the actually capable fighting force - well, that would be considerably less.
Thus it was in Israel.
The reason for the different focus is the reason for there being two accounts in the first place - one looking at historical matters from the Israelite perspective; and one from the Judaistic perspective.
