Does it take longer for synthroid (thyroxine) to work vs. levothyroid?

Not really: Absorption of each thyroid preparation is a little different, and you should not switch brands, if possible. But both synthroid (thyroxine) and Levothroid are long acting hormones, with a half-life of 1 week. I doubt you would notice a difference with regards to onset of action, for example if you were starting to take them for hypothyroidism.