I think your luck will be the same regardless, considering the quality of their "refurbished" products. I'd go with whichever is cheaper.
I'd get it new before I'd buy a pre-owned console from them. I just don't buy used consoles.
Edit: I remember a few years ago a "premium refurbished" DS came with earbuds and screen protectors, while the regular pre-owned didn't
Preowned = traded directly into a store & has never gone to the GS factory (sometimes systems are transferred betweeen stores, a RSB.)
Premium Refurbished = From the GS factory & in a larger box. Traded into a store & for whatever reason sent to the factory for refurbishment. The true coin flips. Note that ALL NEW 2DSXL/3DSXL’s are sent to the GS factory regardless of condition (something on how the stores can’t fully wipe them?) Those are sold in plain white boxes but do come with the charger.