There are many differences in grammars between Cantonese and Mandarin, but the order of adverbs and double objects are particularly obvious:
In Mandarin, adverbs are usually placed before verbs, while in Cantonese, many adverbs can be placed after verbs.
For example, we say “你先出去” (nǐ xiān chūqù ‘you first go out’) in Mandarin, while in Cantonese, we say “你出去先” (nei5 ceot1 heoi3 sin1 ‘you go out first’).
Another big difference is in their double objects. Mandarin and Cantonese have their double objects in the opposite order. In Mandarin, the indirect object comes before the direct object, while in Cantonese, the direct object goes before the indirect object.
For example, we say 他给我钱 (tā gěi wǒ qián ‘he gives me money’ — subject, verb, indirect object, direct object) in Mandarin, while in Cantonese, we say “他給錢我” (keoi5 bei2 cin2 ngo5 ‘he gives money [to] me’ — subject, verb, direct object, indirect object).
Different Expressions and Idioms
Both languages use different idioms and expressions, too, so that even if someone from Hong Kong was able to read a piece of simplified Chinese writing, they may not be able to understand what is actually being conveyed by the writer if idioms or colloquialisms were used (and more so vice versa).
One great Cantonese expression to sum up all of the above, used in reference to Mandarin and Cantonese speakers trying to understand each other, is: ‘the chicken talking to the duck’. Basically, it means that while outsiders may think they understand each other, they don’t really!