What do "Porphyria's Lover" and "My Last Duchess" reveal about the Victorian era that is worthy of our study?

Good question.

The first
thing to say is that the two poems are both dramatic monologues, a style which is
specifically associated with the Victorian era of English Literature - and more
specifically, associated primarily with Robert Browning, who wrote both of the poems you
mention. (The other big exponent of the dramatic monologue in this period is Tennyson,
if you want to research this any further). So it might tell us something about the
period that this particular style - a soliloquy, if you like, by a character who speaks
directly to an auditor (and thereby to the reader) became
popular.

Thematically, though there are a few other things
to say. The first is that both of the speakers of these monologues are murdering
psychopaths! The Duke, in My Last Duchess, has clearly finished off his last duchess in
some sinister way he never explicitly states:

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Oh sir, she smiled, no doubt,
Whene’er
I passed her; but who passed without
Much the same smile? This grew; I gave
commands;
Then all smiles stopped
together.

Similarly,
Porphyria's lover strangles Porphyria to ensure that - very similar to the Duke - he can
possess her forever without her going away. And the way to do this is by - in both cases
- killing her.

The Victorian era was fascinated by the
macabre, and one of the things associated with it in popular memory is foggy, lamplit
streets where murderers and weird deviants roamed at night. Just think of the number of
sinister, crime-related stories to come out of this period: Sherlock Holmes, Dr. Jekyll
and Mr. Hyde and so on and so on - not forgetting the real-world newspaper sensation of
Jack the Ripper, or the emergence of crime magazines to a wider audience than ever
before.

The very repressed Victorians seemed to love things
related to deviant behaviour - whether sexual, criminal or just straightforwardly
violent, and these two poems both allow the reader to travel inside the mind of a
murderer.

The other thing it would be worth thinking about
is the idea of atheism and questioning Christianity - neither speaker, of course, seems
to worry about their behaviour in a religious light. Porphyria's lover even seems to
mock God at the end of the poem:

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And all night long we have not
stirred,
And yet God has not said a
word!

The Victorian period
was a time of a major crisis in faith, often associated with the emergence of the
science of evolution and Darwin's discoveries. It's interesting that religion in these
poems does not feature, despite the fact that the poems themselves explicitly deal with
issues of morality - and you might find that typical of this period of
literature.

Hope it helps!