There's a fair measure of flowery oratory in the Spanish poets, too. It's an occupational disease. But Brodsky's delivery, as I experienced it, was far more stark & stoic. If you listen to some of the Library of Congress recordings, on the other hand, there's a pathos & quavering intimate weak quality to his voice. (I'm a sucker for the sound of RRRussian, I admit. & Italian. Good essay by Brodsky on Montale. He's buried in Venice, near Pound.)
Yet again, one of the things that possibly makes Brodsky difficult to appreciate is that his poetry is also a kind of anti-poetry. He was an admirer of Auden, Cavafy, Beckett - all poets (in VERY different ways) of the flat ironic unpoetic mundane surreal-comic antipoetic manner. Remember, he was one of the grandchildren of the Giants (Akhmatova, Pasternak, Tsvetaeva, Mandelstam). & a near-contemporary of the grandstand Bombasts of the Soviet Cosmos (Yevtushenko, Vozneshenskii...). His prosy antipoetic strictly-metered unmetrical depressing exile as anti-hero mannerisms are a kind of curtain or veil or shield, protecting (as learned in Gulag) his creative process.