I don't think I'll ever understand why Square made the font smaller in the DS version of Chrono Trigger, even though it's meant to be played on a small handheld screen. The SNES font is genuinely easier to read! (SNES left, DS right.)
By comparison, the Japanese versions have exactly the same size font. DS version is exactly as easy to read as the SNES version was. Makes it weirder the English version went for that tiny unreadable font. (SNES left, DS right.)
OK, that's even weirder. Because the DS version is bilingual, if you start the game in Japanese and then swap to English, it has to be able to render Japanese character names alongside English text. Which... means it has room to fit the bigger Japanese text alongside the English. They just don't ever use that room for English.
My best guess is that they made the font smaller so that names can be longer and fit in the UI, unlike the SNES version, because English is generally longer than Japanese. The SNES version worked with the same amount of space for the localization, so nicknames were limited to five characters and many enemies had their names clumsily abbreviated. Dialogue boxes were fine, but the battle UI was very smooshed and crowded. Presumably the smaller text was to help with that. This is all speculation on my part though.