Q:

The difference between 詳しい and 詳細 when used adverbially or adjectivally

While I know that 詳しい and 詳細 both have unique meanings, there are some cases where I am not able to tell the difference between them. Here are two I've stumbled upon:
Adverbially:
我々の研究計画を詳しく述べた
パイロットはその光景を詳細に述べた

Adjectivally:
彼はパーティーについて詳細な説明をした
もう少し詳しい説明をしてください

Is there a difference in nuance, or are they virtually the same?

A:

As (I hope) you could tell from the pronunciations of the two words, 「[詳]{くわ}しい」 is a [大和言葉]{やまとことば} (an originally Japanese word) and 「[詳細]{しょうさい}」 is a Sino loanword. 
As with most other pairs of the two classes of words, 「詳しい」 and 「詳細な」 basically have the same meaning and the 大和言葉 sounds more informal and less technical than its Sino lowanword counterpart.  Perhaps I should write the former as "kuwashii" in romaji for this discussion because we are talking about a spoken language whenever we are talking about 大和言葉.  Japanese was only a spoken language before the Japanese encountered the Chinese. You will keep witnessing this important fact about the "ranks" of the words used in Japanese for as long as you study Japanese.
Thus, there is virtually no difference in nuance, let alone in meaning, between the two words when they are used either adjectivally or adverbially.　Needless to say, only 「詳細」 can be used as a noun in one word.  The Yamato counterpart of that would be two-word-long ---「詳しいこと」.　

A:

As someone who has been learning for sometime I would say that, as a broad rule of thumb for a pair such as this, both mean the same thing in your examples but 詳細 is more formal and more likely to used in written Japanese, especially on technical matters. 
Additional comment:
I think it is also fair to say the "pure Japanese adjectives" such as 詳しい are more likely to have several meanings. The "compound words" such as 詳細 are more likely to have just one meaning, with one character complimenting the other, helping to refine the meaning。
In this case both 詳しい and 細かい{こまかい} can mean detailed but:
詳しい can also be used to mean familiar as in
「Danielくん、銀座に詳しいね」｜"Gosh, Daniel you know a lot about Ginza, don't you?"
細かい has several meanings (I'll leave it to you look in the dictionary) and one other pronunciation,　細い{ほそい}, also with multiple meanings, of which slender/narrow (as in 細い指｜slender finger) is probably the one cited most often in textbooks.  

