Yes, your observation is basically correct. Most na-adjectives are based on Sino-Japanese words (aka kango), which are words borrowed from China along with kanji, whereas most i-adjectives are etymologically truly native to Japanese (yamato-kotoba or wago). Naturally, many i-adjectives are simple and fundamental ones like 大きい ("big"), 赤い ("red"), 重い ("heavy"). On the other hand, na-adjectives tend to be difficult, abstract or technical ones, because such words were not necessary in ancient Japan :-)
Sometimes the same concept can be described using both an i-adjective and a na-adjective. For example an i-adjective 鋭い ("sharp") means roughly the same thing as a na-adjective 鋭利 ("sharp"). In such cases the na-adjective version tends to sound more technical, stiff or formal.
Similar thing can be said for suru-verbs and "normal" verbs. While normal verbs cover most of the day-to-day verb usages (e.g., 歩く "walk", 食べる "eat"), most suru-verbs are kango and can describe more advanced or abstract concepts (e.g., 運転する "drive", 保証する "warrant").