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In this note we show that given two complete geodesic Gromov hyperbolicspaces that are roughly isometric and $\varepsilon>0$, either theuniformization of both spaces with parameter $\varepsilon$ results in uniformdomains, or else neither uniformized space is a uniform domain. The terminologyof "uniformization" is from the work of Bonk, Heinonen and Koskela, where it isshown that the uniformization, with parameter $\varepsilon>0$, of a completegeodesic Gromov hyperbolic space results in a uniform domain provided$\varepsilon$ is small enough.

Rough isometry between Gromov hyperbolic spaces and uniformization