• As mentioned, quaternions don't suffer from gimble lock.
• For a given rotation, there is exactly one normalized quaternion representation.
• Quaternion rotations can be easily combined.
• Floating point numbers have a higher degree of accuracy when representing values between 0.0 and 1.0.

• As mentioned, quaternions don't suffer from gimble lock.
• For a given rotation, there is exactly one normalized quaternion representation.
• There can be several seemingly unrelated axis/angle values that result in the same rotation.
• Quaternion rotations can be easily combined.
• It is extraordinarily complex to calculate an axis/angle notation that is the cumulation of two other axis/angle rotations.
• Floating point numbers have a higher degree of accuracy when representing values between 0.0 and 1.0.

The short answer is that axis/angle notation can initially seem like the most reasonable representation, but in practice quaternions alleviate many problems that axis/angle notation presents.

• As mentioned, quaternions don't suffer from gimble lock.
• For a given rotation, there is exactly one normalized quaternion representation.
• Quaternion rotations can be easily combined.
• Floating point numbers have a higher degree of accuracy when representing values between 0.0 and 1.0.

• As mentioned, quaternions don't suffer from gimble lock.
• For a given rotation, there is exactly one normalized quaternion representation.
• Quaternion rotations can be easily combined.
• Floating point numbers have a higher degree of accuracy when representing values between 0.0 and 1.0.