Too wordy: her side with balsamic asseverations and cloying evasions, his with...

[Gray]

"An acidulous tone had crept into both sides of the conversation, her side with balsamic asseverations and cloying evasions, his with a bite of horseradish astride a malt vinegar redolent of London fogs, fish and chips, and tabloid treacle and gossip (it was, in fact, revolting)."

What does this mean -- in parts and in its entirety?
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First lesson - English, not english. I, not i. ~A student of English

[Milanya]

They both were mean (to each other or speaking of somebody else), but she was more covert and pretentious and he was openly rude.
(Absence of context makes my guess very questionable.)
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con·text - The part of a text or statement that surrounds a particular word or passage and determines its meaning.

[Gray]