The Faith Machine, Royal Court Downstairs, LondonThe God of Soho, Shakespeare's Globe, LondonWittenberg, Gate, London

Questions of faith, capitalism and platonic ideals are thrashed out in Alexi Kaye Campbell's new Royal Court drama

Have you sold out? And if so, would you now say those abandoned ideals – once cherished – simply weren't realistic? Such nagging doubts are at the heart of The Faith Machine by award-winning writer Alexi Kaye Campbell: a keenly awaited Royal Court premiere which itself starts out with great ambitions.

It's not only going to chart a couple's on-off love affair and a father-daughter relationship over 13 years (from 1998 to 2011). The Faith Machine is also a heated debate – between dramatis personae from the US, England, Russia, Africa and Latin America – about the schism-ridden ideologies of Christianity, capitalism and communism.

A New Yorker called Tom (Kyle Soller) is the character who sells out most obviously. At the start of his relationship with Hayley Atwell's Sophie, they are twentysomethings devoted to each other and the arts. He identifies with Hamlet, and is writing a novel about a hero whose calling is to make the world a better place.

Sophie's father, Edward (Ian McDiarmid) is a radical British bishop, residing on a Greek island. He has decided to leave the Anglican communion, because of the Lambeth conference's resolution that homosexual practice is incompatible with scripture. Enraged, Edward calls this pre-Christian prejudice masquerading as morality: a tenet more narrow minded than Plato's Ancient Greek concept of the "third sex".

In Edward's view, the only sin is the absence of love, especially now that love is vital to counter modern societies' market-driven, selfish greed.

As the years pass, Edward becomes severely demented, while Tom turns into a fast-rising advertising exec. Fuming, Sophie confronts him with a choice: if he doesn't turn down a big contract, promoting an unprincipled pharmaceutical corporation, she'll leave him. They go their separate ways and she becomes a campaigning journalist wedded to an academic Marxist – for a time, at least.

At its most winning, The Faith Machine is intellectual and entertaining. Indeed, the disputatious supper scene in Act One is something like Plato's dialogues crossed with Meet the Parents. McDiarmid is especially droll when sardonic, while the atheistic Tom is like a bull in a theological minefield, all gauche faux pas.

Soller is a name to watch. Surely, though, Atwell needs to be more feverish, nearer a breakdown, if her spiel about the pharmaceutical company isn't to sound like an awkward chunk of exposition. The video footage in Jamie Lloyd's production – indicating that Sophie's bust-up with Tom coincides with 9/11 – feels unintegrated too. This play's grand plan, to survey variously challenged global creeds, is admirable. Yet perhaps Campbell bit off more than he could successfully digest in a single play.

Though the storytelling isn't linear, certain elements feel schematic. Lloyd encourages a sentimental milking of some key moments. There are somewhat diminishing returns, too, if you want sharply articulated insights. Sophie's reverentially reported last words state that "against all empirical evidence" she continued "to believe in the human being". What? Are we on par with elves, our existence dubious? Did Sophie actually mean to say "human goodness" or "the soul"?

Ah well, The Faith Machine is a darned sight more lucid than The God of Soho. In spirit, Chris Hannan's new play, veering between shards of poetry and puerile expletives, wants to be a boisterous match for Tony Harrison's version of the medieval mystery plays in rep at Shakespeare's Globe. Phil Daniels is Big God in Hannan's wacky pantheon. He's a rough-and-ready deity, sporting a toga and jackboots, as he opens an inquiry, asking, "Who's the crisis?" with reference to the lack of loveliness on earth and a prevailing ugly mood.

One is, alas, scarcely any wiser by the close. Big God's daughter, the Goddess of Love (Iris Roberts) – jilted by an otherwise unnamed New God – drops out of heaven into contemporary Soho. She hangs out with a homeless lunatic and becomes enamoured of a trashy celeb and her popstar boyfriend. Heaven falls; Big God loses his marbles; and the young lovers ultimately take a leap of (maybe?) faith in each other.

OK, Hannan manifests some freewheeling boldness, but most of his script is bemusingly garbled. Director Raz Shaw resorts to kitsch spectacular parades, strutting cartoon tarts and cameo drag acts. The onstage ska-funk-dub band King Porter Stomp are, at least, having a blast, energising the characters' catchy if self-condemnatory final chorus: "We are so shit, baby."

Last but not least, Wittenberg is a seriocomic, historical-fictional chamber play where Prince Hamlet (Edward Franklin) is a gangly, indecisive undergrad in doublet and trainers. He has got wind of Copernicus's revolutionary model of the universe and is having a crisis of faith. So too is his theology professor Martin Luther (Andrew Frame). Talk about the zeitgeist. They are both egged on by the philosophy lecturer, Dr Faustus (Sean Campion), whom the American playwright David Davalos teasingly portrays as an anachronistic shrink and rationalist, radically questioning all religious dogma.

It is, in fact, Faustus who tells the uptight Luther to write his Ninety-Five Theses as an anger management exercise, then pins them to Wittenberg's legendary church door. Davalos's Hamlet does rather tiresomely spout rejigged Shakespearean soundbites. However, Campion is delightfully impish, clever and funny: a storming performance including tongue-in-cheek cabaret numbers. This gives Simon Gray's Butley a run for its money, in the canon of academic comedies.

Christopher Haydon's production is ingeniously staged in cranky, wooden cubbyhole, with concealed hatches. This bodes well. Haydon is the Gate's next artistic director from January.

'The Faith Machine' (020-7565 5000) to 1 Oct; 'The God of Soho' (020-7401 9919) to 30 Sep; 'Wittenberg' (020-7229 0706) to 1 Oct

Next Week:

Kate Bassett weighs up Decade, Rupert Goold's new production ruminating on 9/11's aftermath