If you remove leaves from plants, when they are still alive, you prevent the plant from photosynthesising, and thus getting stronger. For this reason, I remove leaves selectively, usually when they have mostly returned their nourishment reserves back inside the plant.
I'd consider replanting them, as they may be pot-bound, or the soil may be depleted of nutrients. As last winter was harsh, and the bronze cordylines are less hardy than the green types, it may be that they suffered some freezing damage, and they're still recovering.
That said, if they have enough life force, have good potting soil with nutrients, they should re-establish themselves. If there is decayed parts of the plant, such as the highest tips etc, then this could be removed - otherwise you could leave your plants intact, and just remove leaves when they are almost dead and almost ready to fall off. This will give them chance to generate energy from sunlight, photosynthesis, and strengthen your plant.
Not sure how old your plants are, as mature cordylines can be cut back, and this pruning invigorates them and they usually sprout several shoots, rather than one main one, as younger plants have. As yours are potted, I'm guessing they're still just a year or two old, and these will also sprout back, as yours seem to be doing.
So, I'd generally let the main leaves remain, and not cut back unless there is decay/rot etc. Re-pot giving them some fresh compost, and a good sunny location to reinvigorate and ripen their growth before winter this year.
If winter becomes really cold, consider giving them some protection, to allow them respite, after a hard year.
Hope this helps. Good luck! Rob