I'm a fan of rigging using the rope, but also often carry a cordalette.
Why? I'm a fan of redundancy - tied in via both. It's also easier to equalise. It's certainly easier if you're not alternating pitches, as I really dislike untying and retying in the middle of a wall.
If I was going light and fast, and alternating pitches, I'd leave the cordalette behind.
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