x-height is the height of the lowercase letters, disregarding ascenders or descenders, typically exemplified by the letter x. The relationship of the x-height to the body defines the perceived type size. A typeface with a large x-height looks much bigger than a typeface with a small x-height at the same size.
The typefaces with large x-height render well in busy backgrounds by allowing counters of an optimum size which aid legibility. Especially, the letters with three horizontal strokes such as a,e,s benefit from higher x-height.
The impact of x-height ceases to exist width of the letter is small. Hence these two factors should be considered in tandem.
In the case of letters with two horizontal strokes (o,z,b,d,p,q) large x-height does not affect the legibility much.
Use of large x-height in some cases might lead to misrecognition among the letters if the x-height overpowers the ascenders height (see image ), which usually get suppressed by rounding at the edges because of irradiation thereby decreasing the legibility.
Ascenders play a huge role in letter recognition as compared to descenders.
x-height does not help if the counters are narrow and strokes merge into each other when viewed at an angle.