We address the cost of adding value joins to tree-pattern queries and monadic second-order queries over trees in terms of the tractability of query evaluation over two data models: XML and probabilistic XML. Our results show that the data complexity rises from linear, for join-free queries, to intractable, for queries with value joins, while combined complexity remains essentially the same. For tree-pattern queries with joins (TPJ) the complexity jump is only on probabilistic XML, while for monadic second-order logic over trees with joins (TMSOJ) it already appears for deterministic XML documents. Moreover, for TPJ queries that have a single join, we show a dichotomy: every query is either essentially join-free, and in this case it is tractable over probabilistic XML, or it is intractable. In this light we study the problem of deciding whether a query with joins is essentially join-free. For TMSOJ we prove that this problem is undecidable and for TPJ it is $\Pi_P^2$-complete. Finally, for TPJ we provide a conceptually simple criterion to check whether a given query is essentially join free.