It seems to me that there are often two ways of saying something in Japanese- the kunyomi verbal way, and the compound + suru verbal way. Do you think the latter sounds more educated / formal often?

For example, you could say 終わった　or　終了した, 右に曲がる or　右折しる, 分かった or 了解しました.

Am I way off base with this idea? Just curious.

I see there is a sensible difference in meaning from some of the expressions.
終わる has a softer meaning than 終了する that ensures that the task is completely finished.
Same for 了解. It is adequaded when you want to say you understood something completely, or at least very well. You don't have the same degree of certainty when you use 分かる. Notice that there also 解る and 判る, wich also hold different meaning.

Using Sino-Japanese compounds in Japanese has a similar connotation to using Latinate compounds in English.

In other words, yes jukugo do have a more formal/educated nuance.

Yes, in general using lots of compounds sounds more academic or formal. There are many commonly used compounds that don't give off this impression, however.

This might be a holdover from a time long ago when using Chinese was considered the educated way and normal folk (and women) used Japanese. Also, the on kanji words are said to better for communicating more specific meanings than kun kanji words, so perhaps that lends itself to more frequent use in academic stuff. [simulpost with Jarvik]