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Comparison - Modal verbs
yào
xiǎng

expressing desire or willingness
HSK1 TBCL2

The modal verbs xiǎng and yào both indicate desire or willingness, as if saying “would like to do something” or “want to do something”.

Differences

While being used in the same context, yào sounds more determined and direct, whereas xiǎng implies an intention or desire that may result from consideration, which sounds less direct and more polite.

喝酒。
喝酒。
Wǒ yào hē jiǔ.
I want to have some wine.
(Implication: I have a strong desire to drink)
喝酒。
喝酒。
Wǒ xiǎng hē jiǔ.
I would like to have some wine.
喝酒吗?
喝酒嗎?
Nǐ yào hē jiǔ ma? 
Do you want to have some wine?
喝酒吗?
喝酒嗎?
Nǐ xiǎng hē jiǔ ma? 
Would you like to have some wine?

Compared to yàoxiǎng is more compatible with the tag question kěyǐ ma 可以吗 ‘can I, may I’, to form a polite request.

喝酒,可以吗?
喝酒,可以嗎?
Wǒ xiǎng hē jiǔ, kěyǐ ma?
I want to drink wine/ I would like to drink wine, may I?

Compared to bú yào 不要, the negation form bù xiǎng 不想 is more appropriate for a refusal to make it less direct and more polite.

A: 你吃这个吗?
A: 你吃這個嗎?
Nǐ xiǎng chī zhè ge ma?
Would you like to eat this?
B: 谢谢,我不想吃。
B: 謝謝,我不想吃。
Xièxie, wǒ bù xiǎng chī.
Thanks. I don’t want to have it.

In this use, xiǎng can be modified by degree adverbs or degree adverbial phrases such as hěn 很 ‘very’, zhēn 真 ‘really’ or bú tài 不太 ‘not very’, but yào cannot.

姐姐现在很想休息。
姐姐現在很想休息。
Jiějie xiànzài hěn xiǎng xiūxi.
My elder sister really wants to take a rest now.
我的朋友不太想去打篮球。
我的朋友不太想去打籃球。
Wǒ de péngyou bú tài xiǎng qù dǎ lánqiú.
My friends don’t really want to go playing basketball.