Although these two languages are originally from the same country and they share the same alphabet. Mandarin and Cantonese are not mutually intelligible.
What are the differences?
Mandarin is the official language of China and is used for all business and official policies. The language is spoken in major Chinese cities such as Beijing and Shanghai. Also, Mandarin is the official language in Taiwan and Singapore. On the other hand, Cantonese is spoken in Hong Kong, Macau and in the Guangdong province.
Both languages use the same writing system, so it is possible for a Cantonese to read a newspaper in Mandarin and vice versa. However, there is an increasing tendency to use simplified ideograms in Mandarin, while in Cantonese the traditional writing is still largely used. For this reason, some Mandarin speakers may have trouble reading a newspaper in Cantonese, but the reverse is more difficult to occur. That is, there is almost no difference in writing; but when they read the same newspaper aloud, the differences become clear.
The main difference between Mandarin and Cantonese is the number of tones. Mandarin has four tones, and one more that is neutral. Cantonese has six tones (or 9 depending on how on one counts); which, at least in theory, makes it harder to learn Cantonese. The tones in Cantonese can be high, medium or low, which makes it a more musical language.
Another difference that helps distinguish the two languages is the final syllable. In Mandarin, the syllables almost always end in a vowel, but in Cantonese is more common one syllable ending in a consonant.
Cantonese vocabulary is also known to be more extensive. Cantonese has a broader vocabulary regarding the use of proverbs, idioms and language historical use. Cantonese also accepts better the use of modern slang.
Grammatically, there are differences, but they are minimal, such as change in the order of verbs and nouns.
Which one should you learn?
The one you prefer!!!!
However, in practice Mandarin is the language used by most Chinese universities, and is the language used for doing business. Most materials to learn Chinese teaches Mandarin.
Cantonese is a more interesting language for people who would like to live in one of the regions where it is widely spoken or people interested in the culture of the Canton province. In the largest and oldest Chinese immigrant communities, Cantonese is the main language, so if you have no intention of traveling or doing business in China, Cantonese can be an interesting option.
This amusing video below explains the differences between Cantonese and Mandarin