Each of these Victorian poets has a distinct "voice" or tone, though if we were to find a common element among them, it would probably be that of an underlying sort of acceptance of the external world and nature. It's the way each one expresses this that is unique.
Tennyson, of the three, is the one whose thought is most dependent on religious belief. The opening of "In Memoriam" is a direct statement of the Christian credo:
Strong son of God, immortal love,
Whom we, that have not seen thy face,
By faith, and faith alone, embrace
Believing where we cannot prove....
And yet, the dominant mood is not just sadness, as we would expect for an elegy, but resignation.Tennyson seems to question the positive attitude that the devout of previous ages would have espoused:
If all was good and fair we met,
This earth had been the Paradise
It never looked to human eyes,
Since our first sun arose and set.
It is neither the defiance of a freethinker--as in the Romantic poetry of Byron and Shelley--nor the simple acceptance and optimism of the pious that is seen in Tennyson, but a new feeling we sense bordering on modernism, yet still trying to retain its link to the past and to tradition.
The same is true of Browning, but with the difference that his poetry is filled with a sometimes boisterous vitality and optimism. The speaker in "My last Duchess" moves on, awaiting his next bride and seeming to have no great regret over the last one, and mentioning the bronze of Neptune in the same category as the last duchess's image. The other dramatic monolgues have the same frank, forward-looking quality, one of acceptance, like that of Tennyson, but in a hearty, positive expression:
Ah, but a man's reach should exceed his grasp,
Or what's a heaven for ? [from "Andrea del Sarto"]
Grow old along with me!
The best is yet to be. [from "Rabbi ben Ezra]
Of the three we're dealing with, Matthew Arnold is the least traditional in terms of religion, and the most pessmistic. He regrets the passing of an age when humanity was secure in its religious beliefs:
The Sea of Faith,
Was once, too, at the full, and round earth's shore
Lay like the folds of a bright girdle furled.
But now I only hear
Its melancholy, long, withdrawing roar.
Arnold's verse enters a kind of self-made dream land. Like Tennyson, he anticipates some of the themes of modernism, but in an even closer way, rejecting the real world and its harshness, but alluding to the ancient, classical world more frequently than either Tennyson or Browning. You might want to look at the following additional poems and how they relate to this view of the three poets, or are exceptons that might contradict it:
Tennsyon: "Locksley Hall," and "Tears, idle Tears."
Browning, "Fra Lippo Lippi"