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To add to what the other guy said, rotors (by extension Clifford Algebra) is better. A fatal issue with Quaternions is that while they handle rotations perfectly, things like the norm or cross product of two vectors is messy.

This is unsurprising when several of your coordinates become -1 when multiplied. That's why historically Gibbs Heaviside (dot and cross product) became the dominant vector algebra over quaternions.

Clifford Algebra is the better than both, as you can seamlessly do dot, cross (wedge in CA) and can also embed quaternions within the system. I've heard that it can also accommodate some of the nonmetrical aspects that make differential forms appealing for manifold integration, but that's currently outside of my range of knowledge.