Well, I think "This Time" has more interesting music than "Temporary Home" (which I think depends too heavily on its vocal) - but beyond that, I can't see a lot of depth in "This Time". Although it's by the same team as "Just A Dream" and "Someday When I Stop Loving You" (two of Carrie's strongest songs). TT came across to me as considerably more lightweight in feel and lyrical content.
Therefore, I'm voting here for TH as the more successful song,