This is, of course, highly subjective, but I find "Archer's Theme" entirely too slow and ponderous for a Star Trek introduction.
The theme of Enterprise, and particularly its title sequence, was, "FUCK YEAH! WE MADE IT OUT INTO SPACE!!!" That requires a song with major chords and crescendos.
The mirror universe episodes goes this right, since the theme of that title sequence was "FUCK YEAH, WE MADE IT OUT INTO SPACE AND WE'RE GONNA KICK YOUR ALIEN ASSES!"
"Faith of the Heart" had some triumphant crescendos, but starts off very weakly --- so much so, that the first time I saw it, I thought it was a telephone commercial and started leaving the room to get a drink. I would have preferred a more traditional score: something like an arrangement of the First Contact theme with more umph.