Is Hakka spoken the same in Guangdong and Taiwan?
Although I don't speak Hakka (one of my PhD advisors studied a Hong Kong Hakka dialect, so I have a vague idea about it) I live surrounded by Hakka people, in Guangdong, and I go frequently to Taiwan for work. In Taiwan, I noticed that the HSR announcements in Hakka sounded very different from the "regular" Hakka I can hear in Guangdong.

There's a bunch of Hakka dialects, but you can (over)simplify by saying that Guangdong-based Hakka people speak 梅縣 Hakka (Moiyan Hakka: 梅州, 慧州, etc) while Taiwan-based Hakka people speak 海陸 Hakka or 四縣 Hakka, which present large phonetic differences.

Also, Hakka is influenced by the other main language of the region it's spoken in. In HK, and parts of Guangdong, Cantonese influences greatly the local Hakka dialects -- phonetics, vocabulary. In north-eastern Guangdong, 梅州 and around, where Hakka is the standard and the main language, it's probably less influenced by other languages -- rather the Cantonese spoken there sounds more Hakka-influenced.