Try creating a separate router object for each of them:
package controllers
object PublicAssets extends controllers.AssetsBuilder
object UiDistAssets extends controllers.AssetsBuilder
:
GET /assets/*file controllers.PublicAssets.at(path="/public", file)
GET /ui/*file controllers.UiDistAssets.at(path="/ui/dist", file)
, , , ui, ( - , , .) , -, (, , , .)