If Mandarin-speakers say "meiyou" quickly, it sounds like "mou". If English-speakers say "going to" quickly, it sounds like "gonna".
I wouldn't say all English speakers - someone saying "gonna" sounds distinctly American to me. Around here, something like "gonnae" (which sounds more different than the small difference in spelling would suggest), common usage:
"Gonnae no' dae that?"
I speak both mandarin and cantonese. I think a lot of the 'weirdness' factor comes from actually saying the words. Also there are some words in cantonese that are not in mandarin. For example, in Cantonese, there is 'mou' (the negation of having), while in Mandarin, it'd be pronounced as two words ('mei2 you3). Spoken cantonese in some regards, is easier to pick up than spoken mandarin (definitely easier to cuss in)