Boris Godunov, Coliseum, London; Elektra, Royal Opera House, London

Out of the darkness comes the sound of a lone bassoon; then, barely discernible in the gloom, the floor of the stage seems to come alive. The people of Russia, downtrodden, Tsar-less, drag themselves out of the mud and raise their voices in a plea for deliverance. They sing to order, of course – the Boyars look on – but they sing with blazing conviction.

So begins Tim Albery's new staging of Mussorgsky's original version of his masterpiece. Unvarnished, unadorned, Tobias Hoheisel's barn-like set looks out through great doors to the sodden vastness of the Russian plains. Its all-purposeness is austere but so, too, are the raw materials of Mussorgsky's score, free at last from the misguided adornments of Rimsky-Korsakov and others, and darkly, trenchantly conducted by Edward Gardner. It's a score that underlines the heightened speech and fervent choruses with plain-speaking unisons, haunted solo woodwinds, sombre tuba and shuddering string tremolandi like the icy wind of history across the motherland. Gardner infuses every line with a vital life-force of its own. The brazen, bell-festooned colours of the reluctant Boris's Coronation make a stunning impression.

It feels like a company show driven by strong chorus and ensemble work, but central is the idea that the monk Pimen, chronicling Russia's turbulent history, is who Boris would like to be. Brindley Sherratt commands Pimen's great monologue as if the voice itself carries the weight of history – and it's this element that I miss in Peter Rose's Boris. Yes, it's good to be setting aside the all-purpose histrionics that have beset interpreters of the role, but we always need to feel the terrible burden of guilt beneath the composure of power.

Ultimately it's a moving piece of direction that has Boris, stripped to his nightshirt, led to a quiet death of pilgrimage across his vast, troubled land.

They're washing the blood off the flagstones as the curtain rises on Charles Edwards' much-improved 2003 staging of Strauss' Elektra. The psychological drama has intensified, with this gritty new cast reminding us that Hugo von Hofmannsthal's libretto is one of the most mouth-watering in the operatic repertoire. Add to this the clash of visual styles – the collision between a crumbling classicism and the dusty remnants of fin de siècle chic – and you've a mirror held up to Strauss's perversely sensational score.

That score, with its referencing of musics past, present, and future at the turn of the last century, was thrillingly conducted by Mark Elder and played by the Royal Opera Orchestra. This was Elder's first outing with it and it showed in the sheer shock of newness he conveyed, laying on thick its almost indecent sensuousness.

The music of the words was no less intense. There is nothing quite as satisfying as the spectacle of Susan Bullock (Elektra) wielding the treasured axe that could dispatch her murderous mother. But her dramatic journey to the point at which she finally dons the smiling mask of death and dances for joy is riveting because not a word, not a gesture, fails to ring true. From the terrible images of death in her first scena to the disbelief that her beloved brother Orest (the excellent Johan Reuter) is alive – "a vision sweeter to me than any dream" – the richness of the word colour and her total honesty as a performer adds up to something not just exciting but genuinely moving for once. One or two anxious notes notwithstanding, Bullock shows us that you don't have to be a screamer to play Elektra. She sings everything as beautifully, as meaningfully, as she can.

So, too, Anne Schwanewilms' Chrysothemis, elegantly dressed for better times, and Jane Henschel's haunted Klytemnestra whose grotesque, Robbie Coltrane-in-drag, appearance was truly an extension of her nightmares. Her hysterical laughter on hearing of the supposed death of Orest was just what the dramatist ordered. Not the last laugh, I hasten to add.

'Boris Godunov', to 1 December (0871 911 0200); 'Elektra', to 24 November (020-7304 4000)