Being a Hebbar Iyengar myself, I am much too familiar with the reactions of Kannadigas (people from Karnataka) & Tamilians (people from Tamil Nadu), when they hear Hebbar Tamil being spoken. It usually goes like "that sounds a bit like Kannada but is not Kannada" & "you may call it Tamil, but I cannot understand it at all".
And surfing around, I found this gem of an article
"A BRIEF SURVEY OF HEBBAR TAMIL'S VERB MORPHOLOGY"
comparing Tamil (as spoken by Tamilians) & Hebbar Tamil grammatically.
Although it has a heavy emphasis on the grammatical differences, the examples given serve as a light reading that reveals the subtleties of our language. I would recommend any Hebbar Iyengar who speaks Hebbar Tamil to read this article.