Both are rivals to their respective series’ main characters (Twilight and Ruby) and are the same species as them, both are sharp-tongued but grow kinder in later appearances, both are expert magicians (but Trixie had to train first), both have non-magical arsenals as well, both have best friends (Starlight for Trixie, and Lillian and Laura for Luea), both are shown with teacups (Trixie loves to turn stuff into them), and finally, both ascend to royalty (Trixie becomes an alicorn princess in an alternate universe shown in the IDW MLP comics, while Luea becomes the queen of Jewel Land at the end of Jewelpet Season 7).
Trixie wins this one. Her ability to effortlessly lift a Ponyville-sized dome dwarfs any feat of Luea’s. Being able to catch Rainbow Dash means Trixie can easily keep up with Luea. And finally, Luea may have the superior defense (she’s comparable to Ruby who can survive explosions big enough to be seen from space), but Trixie can just turn Luea into a teacup and smash her (don’t worry, for afterwards Trixie can repair Luea, turn her back into herself, congratulate her on being a worthy opponent, and befriend her).