Hi Angela,
I think you've answered your own question without realizing it!
In your first statement, you say that "increased ionic charge difference between elements increases ionic character". That's the KEY to this question.
We aren't told EXPLICITLY what the electronegativity of cesium is, but IT IS IMPLIED that it is less than 0.8, based on the trend given in the chart. Let's assume that it is 0.7.
So, Cs = 0.7
Cl = 3.0
Therefore, CsCl diff = 2.3.
K = 0.8
Br = 2.8
Therefore, KBr diff = 2.0
So, we can see that CsCl wins!