Deciding which probe to use largely depends on the application.
JC-1 provides a ratiometric measure of membrane potential, where polarization of the mitochondrial membrane is exhibited by a higher ratio of orange to green fluorescence.
TMRE (tetramethylrhodamine ethyl ester) accumulates in mitochondria based on membrane potential, allowing polarized mitochondria to fluoresce and depolarizing mitochondria to lose fluorescence.
In general, JC-1 is better for end-point analysis, while TMRE is useful for monitoring changes in real time.