と～と、どちらが is an expression in Japanese that is made from the following parts:
と - The particle (x2) in its meaning of ‘and’.
どちら - The 丁寧語（ていねいご） form of
誰（だれ） ‘who’, and a slightly newer form of どっち that basically means ‘which’.
が - The 格助詞（かくじょし） (case-marking particle)
This structure is used when the speaker is asking a question about whether someone will choose (A) or (B). It is only used when there are no more than two possible choices.
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ピザとラーメンとどちらが好（す）きですか。
Between pizza and ramen, which do you prefer?
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漢字（かんじ）を書（か）くことと漢字（かんじ）を読（よ）むこととどちらが得意（とくい）ですか。
Between writing and reading kanji, which are you more confident with?
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遊園地（ゆうえんち）に行（い）くのと動物園（どうぶつえん）に行（い）くのとどちらがいいですか。
Between going to the amusement park, and going to the zoo, which is better?
As can be seen above, verbs may be used as part of this structure if they are nominalized with
こと, or
の. Additionally, the polite form does not specifically need to be used, and どっち may be used instead.
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辛（から）い物（もの）と甘（あま）い物（もの）とどっちが好（す）き？
Between something spicy and something sweet, which do you like more?
The second
と itself is quite often omitted, as どちら (or どっち) implies that both (A) and (B) are part of the same structure.
As どちら is the 丁寧語（ていねいご） form of 誰（だれ）, it is also frequently used as a polite way to ask questions about unknown people.
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すみません、どちら様（さま）ですか？
I’m sorry, who are you?
どちらのほう (or どっちのほう) may also be used, but this does not really change the overall nuance. It merely puts slightly more emphasis on the ‘direction’ of the choice. This is similar to expressions like ‘which one are you leaning towards?’ in English.