Some rendering engines like Ogre prefer to use a individual vector based notation for transformations like the following

Split vector notation: Net Transformation is represented by Scale vector = sx, sy, sz

Transformation vector = tx, ty, tz

Rotation Quaternion Vector = w,x,y,z

Matrix notation: There are other engines which simply use a net combined transformation matrix.

What are the advantages of the first notation over the second?

Also for animation interpolation does it work in the first notation that we interpolate across the individual components and use the interpolated parts to get the net transformation? Is this another advantage?