meaning - 小さな vs 小さい/大きな vs 大きい

Is there any difference in meaning between 小さな and 小さい / 大きな and 大きい? I know that they have different syntactical rules, but semantically is there any difference? I was once told that 大きな was more appropriate for non-physical things, e.g. 大きな声.

Answer

Shogakukan's Ruigo Reikai Thesaurus Dictionary has this to say about differences in meaning and usage:

「大きい」は、「夢が大きい」「大きく夢みる」のように述語として、また 連用修飾語としても使うが、「大きな」は「大きな…(名詞)」という言い方でしか使わない。
Ōkii is used as both predicate and as a continuative modifier as in yume ga ōkii, ōkiku yume miru, but ōkina is only used in the format of ōkina...(noun).

物事の程度や、関わる範囲などが大であるという意で名詞を修飾する場合、その名詞が「問題」「影響」など抽象名詞のときは、「大きな」を用いることが多い。
When modifying a noun to mean that a thing's degree or relevant scope is large, ōkina is used more often when the noun is abstract, such as a "problem" or "effect".

There's also a table indicating different valid and invalid constructions, which I've clumsily recreated below. The - indicates an invalid use, while the △ indicates an acceptable but less-common use.

            ～声 | 声が～ | ～問題に発展する | ～影響がある | ～拍手で迎えられる
大きい     〇 |    〇     |               △            |           △         |                〇
大きな     〇 |    －     |               〇           |           〇         |                〇

As shown above, both 大きい声 and 大きな声 would be equally valid. The person who told you that 大きな should be used more for non-physical things might have used the wrong word; given the description above, the distinction appears to be abstract vs. concrete, rather than physical vs. non-physical.

Grammatically, 小さい and 小さな have the same usage constraints as 大きい and 大きな. The thesaurus does not, however, mention any differences in abstract vs. concrete between 小さい and 小さな.