The Tate Modern has just opened the biggest photography exhibition in its history, and it's a goodie – showcasing two of the most influential city photographers of this century, and that's not just because they've been around for most of it. With prints of hundreds of the photographers' works, you can't help but be overwhelmed by the decades of fashion, laughter, smirks, city streets, film, and monuments of life that the space offers. Visit this exhibition with some time to spare, and you won't be sorry.

William Klein's work is first; this exhibition marking fifty years since his first in Milan in 1952 at the Piccolo Theatre. Klein's work overwhelms you as you enter, with huge images of New York and Paris, and the echo of one of his films, a few rooms away, thrumming through the space. What follows are epic amounts of startlingly vivid black and white images, taken in some of the most stunning cities in the world and captured from the ground. Instead of the typical landscapes of these cities, he depicts people: from the rebellious to the rejoiceful, walkways and shop windows, advertisements, cigarette smoke and zebra crossings. The models that feature in some of his most famous work are scattered among the images of everyday subjects – including the renowned Simone & Nina whose unwitting strut along the Piazza di Spagna in Rome is arguably his most recognisable work – which still covers the bumpy walls of many a fashion student's bedroom walls – capturing the culture and flamboyance of the 1960s in one snap of a lens.

Klein's similarity to Doriyama, in principle and art form, despite their especially different upbringings, is demonstrated all over the walls. Klein, born and raised in New York City and a fascinatingly experienced man, took a good deal of time to truly identify his form. Using his lessons from painting, his fascination with faces and his discovery that if your "photograph is not good, it is because you're not close enough" (overheard from Robert Capa, the Hungarian photographer) – which came years before some of his more intimate photographs of children with guns were taken and before some of his blurry photographs – eventually became a crucial element of his artwork, showing New York for the slum it can be. Klein soon moved onto film (such work is shown among the masses of imagery in the exhibition), but never lost his aptitude for his most prominent craft, earning him some prestigious awards including the Grand Prix National De La Photography in 1986 in France, where his work is exhibited regularly, and the Agfa-Bayer/Hugo Erfurt Prize in Germany. Klein is truly a well-traveled worldly photographer, moving from Moscow to Paris to New York, where he would "photograph the s**t" out of his subjects all the way to Vogue Magazine.

Daido Moriyama is equally renowned as a photographer with work spanning as far and wide in time and distance as Klein's. Moriyama's space in this exhibition begins with his more provocative photographs, including Provoke 1 & 2, all of which spawn from his free shooting style in Tokyo (and later, in his early 30s, New York). This work was inspired by Capa, amongst others, whose book he read before he was twenty.

Moriyama believed that photography should not involve artistry – "I just shoot freely", he said –and his gorgeous images that he discovers and captures are an indication of the success of his theory. Moriyama's work is immediately provocative in a way that Klein rarely is, including images of breasts, thighs, piercings and sweat amongst the crowds, train stations (including the harrowing 1977 Platform) and highways. Moriyama's New York images lie right alongside the Tokyo photographs, depicting the somewhat lonely and isolated view he must have had of the busy and tumescent Japan, showing another world entirely.

Some of his more intimate work includes Matsumatsushima, an image of a crazed young podgy boy staring maniacally into the camera. The documentary-type films that accompany the exhibits give the visitor a broader understanding of the work (even if you don't wish to read the plentiful supply of literature available just before the stocked gift shop) and the men themselves. Moriyama's words are fascinating, including his admittance of using a compact digital camera rather than the beast of an analog camera you see so many amateurs lugging around their necks. Cities, to him, are "enormous bodies of people's ideas" and he finds the world "an erotic place" – facts that resonate in every photograph.

This exhibition is sure to be a hit with anyone passing through the Tate's magnificent walls. The pictures that these men take highlight parallels between them, with so many similarities spawning from both identical and diverse ideas and ideals. The William Klein and Daido Moriyama exhibition is a fascinating sightseeing time machine: find the time to embrace it.

William Klein/Daido Moriyama, at Tate ModernHeather Deacon reviews William Klein and Daido Moriyama at Tate Modern.5