The revamped RSC showcase has its faults, but it will make watching Shakespeare a more rewarding experience

Can you spend a hundred million pounds on nuance? Or, rather, can you justify it? Should such sums be shovelled at achieving intangible effects, which might otherwise help house the poor or save sports programmes in schools? Or, next to the billions vanishing into faceless corporations under the private finance initiative, or bailing out Ireland, might it not be money well spent?

This is the question raised by the revamp of the Royal Shakespeare theatre in Stratford-upon-Avon, where the main consequence of £113m of expenditure is a difference measured in yards in the position of actors relative to the audience. Its success will be defined by the timbre they feel able to adopt and the detail of their expressions observable by spectators.

To be sure, the tab covers other useful things: better access, less cramped foyers, bars, a rooftop restaurant, new dressing rooms with a view of the river Avon. It includes the cost of building the temporary Courtyard theatre to house performances during building works. Of the money spent, £40m is not public, but from benefactors led by Lord and Lady Sainsbury of Turville. But, ultimately, the main object was to replace the 1932 auditorium, designed by Elisabeth Scott, with another that would work better, while retaining and modifying the rest of the building.

Scott's space, at the request of her clients, mimicked the then-ascendant medium of cinema. It fanned out from a proscenium, widest where it was furthest from the stage, meaning that generations of school parties would be introduced to Shakespeare as the distant oscillation of smudges. The new theatre has a thrust stage and a very thrusting one at that. It projects the action deep into the auditorium, with the audience stacked around it in stalls and galleries, in conscious imitation of the courtyards and high-sided theatres where Shakespearean drama was first performed.

It is, says the Royal Shakespeare Company's artistic director, Michael Boyd, "a one-room space for performing Shakespeare, rather than one lot of people in one room looking at another lot of people acting in another room". The new theatre is smaller than the old one, with 1,040 rather than 1,400 seats, but the maximum distance of spectator from stage is down from 27 metres to 15 metres.

The acoustics, fine-tuned with the help of experience from the temporary Courtyard theatre, promise to be immaculate. A basement, expensively wrested from the Avon-soaked mud beneath the theatre, and a fly tower filled with a "wedding cake" of gear, will lay on a director's dream of potential effects. The bare boards of the stage are deceptive, sustained as they are by bionic infrastructure.

The RSC have bet heavily that the thrust stage will be the way of the foreseeable future. They already had one, in the much-loved 1980s Swan theatre, which lies end to end with the new auditorium, and has been little changed by the new works. Sir Peter Hall has muttered that they're overdoing it. Boyd retorts that the new theatre is sufficiently adaptable to achieve Hall's preferred form, which is a more shallow thrust.

What the RSC is not now trying to achieve is a theatre that can do everything. A decade ago, a previous attempt was made, by the then artistic director Adrian Noble and the flamboyant architect Erick van Egeraat, to create a place that could handle both proscenium and thrust. Hugely complex, this would have obliterated all the theatre's existing buildings and some of the open space around them. Eventually, the scheme crashed and burned, to be replaced by the more sober project we have now.

The new work is collaborative and consensual to a fault. The RSC says it chose Bennetts Associates, the architects, because they were good at the workshops they arranged between potential architects and theatre people. Rab Bennetts, the leader of the practice, stresses the importance of "managing meetings and being consultative". His interventions are commonsensical, deferring to both the drama of performance and the retained parts of Elisabeth Scott's art-deco building. They help the building to flow better inside and to connect better with the surrounding town.

The play's the thing, in other words, and the ensemble counts for more than the star. If there's one character in the team who is more equal than the others, it's Michael Boyd, who, in contrast to his cautious colleagues, declaims to the press with actorish fluency and flourish. His vision of performance drives everything; the architecture serves to achieve it.

But there's something missing. Architecture and theatre are rivalrous companions, in that each proposes a universe into which the inhabitant or spectator is invited to enter. Modern architecture also favours the honest exposure of the stuff of which it is made – plain steel and bricks – which is at odds with the illusion and greasepaint of theatre. To say a building looks like a stage set is usually an insult. The very best theatres, old or new, give due prominence to the stage while also conjuring in the auditorium and foyers their version of Prospero's cloud-capp'd towers and gorgeous palaces, which can be done as well by the gilt and cherubs of an Edwardian music hall as by the rough walls of a converted warehouse.

Bennetts's theatre doesn't do this. He uses handsome steel and untreated oak, but their qualities are muddied by the low light of the auditorium and you have to look hard to notice them. In the foyer, a distressed wall of the old building has been left fashionably exposed, but it doesn't join up with the other surfaces to make a coherent space. Architectural expression is largely outsourced to the theatre's new 36-metre campanile, a slightly gawky assembly of brick and glass.

Problem-solving and process over-dominate. The theatre is what the RSC call "an optimal environment for experiencing Shakespeare", a phrase that could only make the Bard cringe. Contemporary architecture tends to oscillate between the iconic and the efficient and the RSC, in going from van Egeraat to Bennetts, has experienced both. Given that choice, it has made the right one, but it has missed out something else, which is the making of places with their own identity and life, complementary to that of the drama.

For all that, the main aim has been achieved. Subtlety and spectacle and the wrapping together of audience and action will all be possible as never before. Is this worth £100m? If the arts are worth investing in at all, and if that investment should support the best possible realisation of art, then the answer has to be yes.