'Power and possession' are certainly crucial to the speaker, the Lover, but in the context of this dramatic monologue probably have less to do with the desires of men in general (and thus with sexual politics) than with the 'character' set up for the speaker himself. This poem's concern with possession, and with the Lover's proud and jealous desire to kill in order to capture the moment takes up a theme we see in some of Browning's other work (famously, in 'My Last Duchess', which I suggest you look at.) The 'moment made eternal' is something which preoccupied other Romantic poets, especially Keats. See his 'Ode on a Grecian Urn' .
Essentially, however, this is a Gothic, and shocking, record of the Lover's madness, concerned with his own peculiar psychology (psychopathology?) in which he tells us, in very matter of fact terms, how he 'found a thing to do', and 'strangled her', before embracing the corpse whose eyes he has reopened, and who can now look on him with 'no stain'. We can certainly guess at a back-story, that there may be an obstacle to their union: perhaps she is married already; perhaps there are social reasons why they cannot be together - the fact that he lives in a cottage alone, and she is dressed like a gentlewoman in cloak and shawl, wearing gloves, suggest a difference of 'station' - but we are not told directly. Chiefly, this is about the Lover himself, who would rather kill Porphyria at the moment he realises she will submit herself to him - to freeze the moment, as it were - rather than have her challenge his pride or 'scorn' him again. By killing her, he has her forever, and for this night at least, he remains (by his own lights) unjudged by God.
Because dramatic monologues are in themselves 'snapshots', a framed fragment, we can only guess at what might follow. (Presumably, this moment cannot possibly last: the corpse would begin to decay; he might be caught and arrested.) There are multiple ironies here, not least in what we might be expected to believe: dream coming true, and captured - but perhaps there is much in this to suggest 'dream' in any case. The Lover would rather kill the beloved than make love to her in any ordinary, or passionate, human way. In fact, the Lover's 'passion' is almost inhuman in itself - note that there is no dialogue between them: when she speaks, he remains silent - and concerned less with her than with how she regards him.
You need to examine the language closely. The Lover's heart swells - surely indicating erotic arousal - but he 'debates' what to do, as if this is a matter for sane consideration. There is much to suggest the Lover's necrophilia - how do you read his 'burning kiss' on her corpse-face, compared with his passivity and silence when she is alive? The tone is surely almost comic, too - that 'I found a thing to do' which undercuts the idea of passionate homicidal impulse almost completely is a case in point, but probably underlines the Lover's insanity best of all.
I think this poem deserves many readings, and I hope you discover more as you go. Hope this has helped!