Although both Tennyson and Browning are important Victorian poets, they differ in background and style.
First, Tennyson was a member of the British upper classes with wealthy grandparents, but due to an odd inheritance arrangement, his father was a relatively poor clergyman. The contrast between his own circumstances and wealth of other members of his family was something he felt acutely. He was educated at Trinity College, Cambridge and had a solid knowledge of Greek and Latin, as was common with members of the upper classes in his period. His work reflects a deep engagement with classical culture. He became immensely popular, was appointed Poet Laureate, and granted a peerage. By contrast, Robert Browning came from a family of middle class dissenters and although admired by a small circle of intellectuals, he never achieved Tennyson's immense popularity.
Often Browning is considered the more innovative of the two poets due to his often unusual syntax, but actually under his mellifluous and fluid surface style, Tennyson is perhaps even more radically innovative. Both poets wrote dramatic monologues, but while many of Browning's narrators prove completely evil, Tennyson's often demonstrate a sort of moral ambiguity. Both poets experimented with writing in dialect and using nonlinear or complex narrative structures. While Tennyson often explores classical and medieval themes, many of Browning's best known poems are set in the Renaissance.
While Browning's poems reflect a wide range of emotional tones, Tennyson is best known for his evocation of melancholy, although he also could write entertaining poems in dialect such as The Northern Farmer: New Style.