Now we keep the destination cards secret, but put player colored markers on the cities corresponding to the endpoints of their destination cards. (A third party sometimes needs to help her put out her markers) Since the cards themselves are still kept secret, the other players don't know how the cities are to be connected.
This variant ends up being a bit more deliberately cutthroat as you now know something about your opponent's destinations, paving the way for more intentional blocking. Surprisingly, my budding gamer prefers it that way.
Not sure how it actually matters. Except in extremely rare occasions your whole network is actually connected, right? What I mean is that 99% of the time, having a (shuffled) list of ticket endpoints is exactly equivalent to having a list of tickets.
(This said the marker thing for non-readers is still a good idea.)