As for technique: Browning and Carlyle both root the reader in the moment and equate present reality with past, future, and eternal realities by linking the present with the Classical past. As Carlyle puts it:
Phlogiston is replaced by Oxygen, and the Epicycles of Ptolemy by the Ellipses of Kepler, so does Paganism give place to Catholicism, Tyranny to Monarchy, and Feudalism to Representative Government — where also the process does not stop. [Norton 961
Compare Browning in Aurora Leigh:
Helen's hair turned grey
Like any plain Miss Smith's who wears a front;
And Hector's infant whimpered at a plume
As yours last Friday at a turkey-cock.
Carlyle's thrust is that we have no more arrived at truth today that we had in the past, when the obsolete ideas he refers to were thought to be correct; Browning's is that even heros of the past were no more than human, and were subject to the same trials and fears we experience today. Both authors, in a characteristically Victorian manner, bring the past down to the level of the present, and vice-versa.
Both Browning and Carlyle cast off the traditional method of reading the Bible as literal truth and fell away from established religious institutions. Disaffection from standardized Christianity is evident in "Characteristics" in several places, especially when Carlyle discusses the demise of religion (Norton 956), and in Browning's disparaging treatment of Aurora Leigh's aunt's religious convictions and affectations (Norton 1084-5). Bishop Colenso's The Pentateuch and the Book of Joshua Critically Examined and certain geological findings indicating that there had not been a flood (as the Bible put forth) that covered the whole of the earth's land mass were among several scientific and scholarly advances that undermined faith in traditional Christian doctrine. These scientific evidences of the historical inaccuracy of the Bible combined synergistically with philosophical ideas of the Victorian era (of which Carlyle was a seminal thinker) to produce a uniquely modern perspective of the world. The Victorians laid the groundwork for later ideas of the death of God. (Norton 956)