I prefer Ultramar, as there is a single car deck, more or less at dock level. Transcaribe is a narrower, taller ship with two decks, and visibility is not good, especially when going down the ramp between decks.
Depending on where you're going in Tulum, you might consider leaving the card on the island, taking the passenger ferry to PDC, and then ADO Bus to Tulum. The bus stops at the entrance to the ruins, and downtown. This also has the advantage of more frequent (more convenient?) ferry service, versus the 6x/day for the car ferries.