"visual style"?
I mean, Clark style is the kind of private snapshots of with pretty low artistic touch. Pretty bleak and lame tonality, like just being someones hobby in times when b/w photography was the norm. He would take snapshot to film and have paper print of it? And context and intent would only make it "art". Otherwise it would be just relatively low quality snapshot of someone hanging around in same flat as he was, possible doing dope. Just document of his troubled life at the time. I mean, if we talk about TULSA?
Manns visual style is exaggerated craftmanship and celebration on magical imperfect accidental artifacts caused in the process. Some are accidental shots, but many are staged into perfection and very little "documentary" in way mentioned above. A long time shot on glass negatives or later even glass positives (the black glass being the photo itself), with utmost care on tonality and making unique prints. Also prints themselves would be often utmost quality unique hand made prints of archival quality.
I can't see anything same in visual style. One could rather say that Mann has more common with for example Jock Sturges. But also their similarities are most of all vaguely, crossing in points such as "successful & known artists" and "using nude people". But their approach and intention, not to mention actual results are far far away from eachother. This is also well illustrated in amusing story Sturges tells in documentary about him. Incident what happened at Mann's house. Some kid fall flat on his nose, with result of nose-bleed. Every other high class photographer acted on parental instinct and seek best way to solve this situation. Comfort, stop bleeding, etc. but not Mann. She would first ran to get her camera, to get the photo of kid with blood running down the face. And it disturbed Sturges, who's aim is, of course, to capture the utmost natural beauty of human - or should it even be said - person?
Sturges would shift from large format film into digital as soon as technology was advanced enough. Mann would go even further to technic not after film, but BEFORE film existed. And it's hard to get past the technique and craftmanship, when it's nearly reaching towards pictorialism, while these two guys mentioned here, just more or less capture the existing reality with quite regular means.
Of course, this is more of situation similar to someone saying Pain Jerk sounds like Incapacitants. And on some level, yeah, but really not at all.
I think Clark was much better movie maker than photographer. I think reprint of Tulsa is found quite cheap as A4 size paperback book. If one likes his movies, it's not a bad purchase, but I wouldn't put it very high on "must have" list.