My only background on this subject is a course I took as a grad student, so take my answer with a grain of salt:
The reason that some methods transform the DAG to a tree because some algorithms work on trees but do not work on graphs with cycles. For example, belief propogation is guaranteed to converge on a tree after every node received two messages. On general graphs, on the other hand, no general convergence theorem is known, and we know that convergence occurs only in some special cases. Intuitively, the reason is that on a general graph, a message that goes through a cycle can loop in it indefinitely, each time changing the information stored at the nodes.
Regarding under what circumstances it is recommended to transform the graph into a tree: In the process of transforming the graph into a tree, every node of the new tree is identified with a set of nodes of the original graph. The size of the maximal set with which a node is identified (in the best decomposition) is called the tree-width of the graph. Now, the complexity of belief propagation, as well as other algorithms, is exponential in the tree-width, so you want to transform the graph to a tree only if the tree-width is sufficiently small.
Unfortuantely, it is $NP$-complete to compute the tree-width of a graph exactly, but there are some approximation algorithms. You can read more about it in Shiva Kintali's blog: