The truth is it is not easy to distinguish just from those written words alone. BUT, there are certain expressions that may be common in Cantonese but might sound awkward in Mandarin (as of the other dialects). So usually, those are hints. Moreover, Cantonese (back when I was in school), the native written form is Traditional Chinese, whereas Mandarin, the "standard" written form is Simplified Chinese, because it originated from China. So going by the picture itself, although it's possible that it might be in Mandarin, if I were a betting man, and my only two options were between Cantonese and Mandarin, I would have picked Cantonese.

cantonese or mandarin Actually they can change，if you see it， they just words，it's not easy to distinguish， but if u listen it， it's easy.

I would also be curious to know if there's a way to tell that this is in Cantonese without hearing the song. As far as I understand, both Cantonese and Mandarin songs are usually written in standard Chinese, so I would assume that the lyrics, in written form, would be equally understandable to both Cantonese and Mandarin speakers (as long as they can read traditional characters). In some cases, the lyrics to a song will only rhyme properly in one language or the other, but I think in this case 愁 and 憂 rhyme equally well in both Mandarin and Cantonese, don't they? So is there a way to tell just by looking at the lyrics in the linked image (又有喜 又有愁 就算分不清歡笑悲憂) that the song must be in Cantonese? I assume this is what Ng is asking about.

Of course,it's cantonese（粤语）。Most of Chinese can't understand what she is singing. But this song is still very popular.