This comparison is usually framed as a preference. It is better understood as two tools for two jobs on the same face, and the reason is the difference between the two places concealer goes.
The under-eye is thin, mobile and concave. It flexes thousands of times a day and it has somewhere for product to collect. What it needs is the least possible material, spread thin, staying flexible — which is a liquid. Liquid concealers carry more water and slip and less wax, so they spread further per unit of product and they do not set into a film that can crack.
A cheekbone or temple spot is the opposite situation. The skin barely moves, and the job is to put a dense dose of opposing pigment in a precise few millimeters and keep it there. What that needs is cream: more wax and pigment, less water, so the product stays where you press it instead of spreading.
Using each in the wrong place produces predictable failures. Cream under the eye is too much material in the least forgiving spot, and it creases. Liquid on a spot spreads thin, loses its pigment density and the mark shows through — which is the same failure as blending, arrived at by a different route.
There is a third texture worth naming because it has become common: the serum concealer, which is a liquid taken further — more water, more slip, even thinner. On a crepey or heavily lined under-eye it is frequently the best option on the market, for the simple reason that it is the least product.
