I have a particular fondness for fonts that have larger x-heights than those that do not, which is such a sweeping generalization to make, that I couldn’t tell you specifically why other than in my head I know exactly why.
Ultimately for what I do, mostly creating logo designs, font selection is frighteningly crucial as you only have a few letters and these take the stage and spot-light.
If you make the wrong font choice for the logo, then you’ll find it’s really wrong.
Making a choice of large or small X-height to create the right message for a logo design involves understanding of: technical specifications, subjective aesthetics, overall context and finishing up with that well trusted gut-feeling.
Does a large x-height make fonts more legible? is a great read by Ralf Herrmann and will certainly gives you some things to dwell over when you come to choosing your next font