A. 今天上午他很快地吃完了饭 // B. 今天上午他饭吃得很快
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The main difference between these two constructions is that the adverbs in 地 construction describe the MANNER, MOOD or METHOD in which the actions are carried out; but the adverbs in the 得 construction are the DEGREE or RESULT of the actions and sometimes they can refer to the objects of sentences, e.g., 他吃饭吃得很多 the adverb 很多 refers to 饭. The emphasis in the (地) sentence "A" is very much on how he ate the meal. In other words, the stress is on his MANNER of eating the meal(action), but the result of that might not be necessarily very fast. The "B", (得) sentence implies that he only took very little time to finish the meal.
So, in your sentences:
他复习汉语复习得认真。
The degree in which he reviewed was sincere/serious/studious. As a WHOLE, his reviewing may have been sincere. But maybe he took 5 years to do it and during that 5 years, he didn't 认真地复习汉语. The result of reviewing is sincere and hardworking-like.
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他认真地复习。
There is no result here, just saying his manner, method, or mood of studying is serious/sincere.