When expressing a superlative meaning ("the most ..."), what is the difference between the usage of もっとも and 一番？ (e.g. もっとも大きい vs. 一番大きい)
Simply, 一番 is colloquial/casual, and 最も is formal/technical. Oh, this is one of the rare cases where 漢語 words are more informal than the 和語 versions.
In addition, 最も can only function as a modifier, while 一番 can work as a noun which means number one.
- 私が一番だ。: OK
- 私が最もだ。: NG
When expressing superlative, both もっとも and 一番 have the same meaning.
Here are the definitions of もっとも and 一番 according to デジタル大辞泉.