Verdant describes the land; whereas lush describes the quality of the vegetation growing on the land.
"Verdant" comes from the Latin viridis which means "green". You can describe a piece of land or ground as "verdant" if it is green from the vegetation (ie grass) growing on it.
But "lush" describes the quality of the vegetation itself - that it is luxurious, abundant, flourishing.
This ngram is interesting - it seems that in the past it was more common to describe a valley as "verdant", but in more recent times there is a trend to describe a valley as "lush". However these are very small numbers, so I wouldn't place too much emphasis on it.
I would say that either of your suggested options are fine and convey the same meaning. "Verdant" might not be as widely used or known, but, also "lush" has taken on a secondary, more informal use in modern British English. Saying "lush green valleys" though makes it very clear you are describing the grass and vegetation.