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• Catmull-Clark subdivision surfaces are the industry standard. It is a quadrilateral-based subdivision scheme, and works best with control meshes that are comprised mostly of quads - any non-quad geometry is immediately converted to quadrilaterals on the very first subdivision step. They generally good for most situations and have no special concerns when it comes to texture filtering.
• Loop subdivision surfaces  (Not Supported in XPU) is a triangle-based scheme, which is optimized for control meshes that are entirely triangles: they tend to require less memory than Catmull-Clark scheme. However, due to the nature of triangles, derivatives can be discontinuous from face to face, which may lead to texturing artifacts that require extra effort to solve.
  
• Bilinear subdivision surfaces simply render high level 4-sided faces to bilinear patches, and subdivides all n-sided faces to n blps. Like other SubdivisionMeshes it supports all hierarchical edits, is guaranteed to be watertight, can be used with the Rix Subdivision API, and can be used in conjunction with PTex.

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