A teacher's note for the lesson on expressing preferences with "like ... better than..." says that "It is also possible to use an infinitive after like; the text presents only the gerund pattern here. Using an infinitive with like ... better than can lead to awkward sentences and confusion with placement of the to. Native speakers would be likely to avoid such structures and, therefore, they aren't presented here.
Recommended Pattern in the text:
1. I like tea better than coffee. (Like NOUN better than NOUN)
2. I like drinking tea better than drinking coffee. (Like GERUND better than GERUND)
My question is: why would the infinitive be awkward?
3. I like to drink tea better than to drink coffee.
4. I like to drink tea better than drink coffee. (no need to repeat the "to")
5. I like to drink tea better than coffee. (no need to repeat the same verb)
Are sentences 3, 4, and 5 awkward as the teacher's note above suggests?
I can understand why prefer X to Y has to be a gerund and NOT an infinitive because of the "to" already in the sentence.
6. I prefer tea to coffee. OR (NOUN to NOUN)
7. I prefer drinking tea to drinking coffee. (GERUND to GERUND)
*8a. I prefer to drink tea to to drink coffee. (Awfully bad structure because of the preposition to and even if we delete the second infinitive to, it will still be bad: *8b. I prefer to drink tea to drink coffee.)
But (If we choose to use an infinitive, we will need to change "to" to "rather than":
9. I prefer to drink tea rather than to drink coffee.
10. I prefer to drink tea rather than drink coffee. (repetitive to deleted)
11. I prefer to drink tea rather than coffee. (repetitive to drink deleted)
I hope my analysis of "prefer X to Y" is accurate. If so, we can focus on the question:
Why would the infinitive be awkward with "like X better than Y"?
Source: Fundamentals of English Grammar, 4th edition