In Titus Andronicus and Romeo and Juliet, is the cathartic effect of the tragedy intensified or diminished by the pervasive atmosphere of brutality and vulgarity?

One could argue the tragedy is intensified in both cases. Part of what makes Romeo and Juliet so poignant is the contrast between the purity of Romeo and Juliet's love and the violent, hate-filled society that thwarts their ultimate happiness. The lovers try to find a way to be together and live in Verona (and in the good graces of their families, the state, and the church), but the feud and Romeo's own violent reaction against Tybalt destroys their dream.
The vulgarity of the other characters only serves to make Romeo and Juliet's love seem nobler. Mercutio makes bawdy jokes and seems to view sex as a mere carnal act. The Nurse also makes comical references to sex and breast-feeding, which causes Juliet to blush uncomfortably. However, Romeo and Juliet's wedding night is not treated with irreverence (see the lovely imagery of Juliet's erotically-charged "fiery-footed steeds" speech in act 3, scene 2). Their parting after the consummation is tender and sweet. All of this serves to make their love seem more fragile and their final tragic fates more emotionally devastating.
Unlike Romeo and Juliet, in Titus Andronicus, the characters seem to accept the violence of their world, rarely if ever hoping for anything better. From the very first scene, Titus kills one of Tamora's sons in cold blood as a sacrifice, despite the entreaties of Tamora herself. His actions in that opening scene help set off the cycle of vengeance which dominates the play.
The brutality of Titus Andronicus is contrasted with the heroic qualities of its titular protagonist. Titus is brave, patriotic, and devoted to his family. He weeps and laments when he learns his sons have been killed and his daughter has been raped. He is not a total monster, which makes his descent into further brutality tragic. As a revenge tragedy, Titus Andronicus shows how the fulfillment of vengeance does not lead to happiness or peace. It only leaves the stage littered with bodies.
(Of course, some might argue in Titus' case that the over-the-top violence could be played as darkly comedic and that this undermines the pathos of the characters' situation. However, not all modern productions of the play take this approach.)