My ponytail is a starving orphan compared to your big, lush ones. It's about 6ft. from the base of a huge oak, and gets no direct sun or TLC from me except maybe a bit of fert when I treat the Heliconias in that bed. Bet those ones in your Lima picture are in pots and probably starving like mine.
Both yours and mine have summer growth going on now, hence the crazy 'punk rocker' topknots. I think in winter mine would look more like your mystery plant.