I think the main problem with option B is the article "a"
aspirin prevents blood clots just as well as does a commonly used and a more expensive blood-thinning drug
the second "a" kind of implies that there are two drugs rather than one.
On the other hand if you remove modifiers in option A is clear
aspirin prevents blood clots just as well as acommonly used and more expensive blood-thinning drug does
articles precede nouns. so if you have "a/an X and a/an Y",
...
aspirin prevents blood clots just as well as does a commonly used and a more expensive blood-thinning drug
the second "a" kind of implies that there are two drugs rather than one.
On the other hand if you remove modifiers in option A is clear
aspirin prevents blood clots just as well as acommonly used and more expensive blood-thinning drug does
articles precede nouns. so if you have "a/an X and a/an Y",
...
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