Both.
I display all of my Larges and Huges. I also display my growing collection of custom repaints in pride of place along the top of my dual monitors. The remaining pieces -- about 2150 of them so far -- are sorted into 40 categories and stored in 800-count card-boxes, which themselves are stored in three-by-four card-houses, which are kept on shelves within reach of the DM-Chair.
My categories are things like, "Weapon-and-Shield Warriors," "Rangers, Rogues, and Dual-Wielders," "Orcs 1," "Orcs 2," "Aberrations," and so on.