The first option, "even though pets are great stress relievers, they are a lot of work" has the more accurate and effective transition word (even though).
"Even though" is a transition expression that is used to convey the idea of concession.
In this case, the use of the concessive "even though" indicates that both propositions are correct: pets have the ability to relieve your stress, but they demand much of your effort to take care of them.
