I think that one particular point of view that might be needed in any comparison between both poems is the fundamental approach taken in each to the natural world.  In Tennyson's poem, there is a clear point of view in the brook speaking.  Tennyson personifies the brook as one that outlasts the wills and lives of men.  It is living history.  With its refrain of "men may come and men and men may go, but I go on forever," the brook speaks of an eternal nature that is timeless and eternal.  In Ramanujan's poem, the point of view is more about the poets, themselves, that write about the river in Madurai.  The poet's focus is not as much the natural world, but rather the retelling of it.  In this, there is a sense that the words of the "old and new poets" miss out on a part of the river's nature in terms of describing its destructive quality.  In Tennyson's poem, there is no need for poetic voice because the brook itself is the quantity that speaks, outlasting the words and narrations of the poets. 

Through this analysis, there is another form of comparison which is the view of the natural world, in general.  The Tennysonian view of the "the brook" is serene, almost tranquil in its stately beauty and grandeur.  Verbs like "murmur," "linger," "chatter," "wind," and "slide" help to bring out the personality of the brook, something of beauty and a sense of natural beauty.  This is not the case in Ramanujan's description.  The river is described in one of two ways.  The first way would be its dried and barren state, complete with its "baring" of "sand ribs" and its "trickle" to reflect how much it dried.  Then, the flood of the river happens, and Ramanujan's description is one of brutality in terms of dead pregnant women and twins and the cows that were swept up in its waves.  The lack of reporting of this destructive element is almost as bad, if not worse, than the natural calamity, itself.  In this, another fundamental difference is evident in both poems.