I have been checking both these cards out for an upcoming 4 day stay in Lisbon. The Lisbon card, sounds like all transportation (metro, buses, lifts, trams) plus reduced fare to museums. The Viva Viagem sounds like the preloading / reloading zapping car, used on transportation only.
I saw on the Viva Viagem card site, that they have a 6 euro 1 day pass, used again on transportation only. I emailed the Lisbon Visitor Center and asked about this card. They wrote that I could use it in Lisbon, going to the beaches of Cascais and Estroil, and to Sintra. I plan on asking again at the Metro Station to make sure, otherwise I plan on using the zapping Viva Viagem card only.
We are the from a Friday to Tuesday. Many things are closed on Monday, Sundays some things are closed too, and check about the free admission, because I noticed some changes from my previous visit. Now, the free admission, to some places, is only on the first weekend of the month.
Check out the Lisbon cards website and see if its worth the discount- not all museums are on their list. For our family, the list of museums and sights on the Lisbon Card didn't marc up with what we wanted to do.
Hope this helps.