As for what kicked off Zelda and FF, both were relatively fresh and high quality for their respective platforms. Zelda was especially well marketed too. Both went on to deliver banger sequels in gen 4, multiple for FF. Building upon their predecessors in huge ways, being some of the most critically praised games of the gen.
Gen 5, OoT translated the series to 3d pretty well and in a lot of ways served as a blueprint for 3d action adventures to follow. Impressive for its time and very influential. FF7 was cranked on production values, became the intro to rpgs for many console players, brought the series and genre into a whole new level of mainstream appeal.
And ever since, they've both mostly done well to reinvent themselves and maintain quality in one way or another.
Zelda (pre BotW) admittedly leaned on the formula established by ALttP a bit more than I liked, but was probably more consistent for it. Still a fairly fresh experience from one game to the next. And of course BotW took the series fame to new heights. To the dismay of some with its sweeping changes, but I'm a fan lol.
FF, the path has been less stable, reinventing the wheel a bit too much imo. Some entries unrecognizable from the series roots. And while production values remain high, arguably that's too big a focus tbh. High quality coat of paint on a lesser quality game. Such a random series at this point, but the brand remains strong.