There's a setting called transparent sorting, and you can pick between three options: per triangle, per strip and per pixel. Per pixel is the most accurate, and if you select it in the standalone Flycast, an additional setting will appear, letting you change the amount of maximum layers, which can improve performance for some games. In tico and Retroarch there is no maximum layers setting, meaning that when selecting per pixel the games will always look as best as possible, but performance may not be as good. And while per pixel is not mandatory for all games, some will look bad without it, for example, in Sonic Adventure, Sonic's hands will look messed up, and in Daytona USA your car will be missing some textures.
TLDR: tico's Flycast and the standalone version perform the same, but some games look better in the standalone version.