What repairs faster when injured: white matter or grey matter?
Short answer
As @BryanKrause indicates, neither answer really makes sense.

Background
This is basically per the answer of @BryanKrause. Myelin is the stuff that forms the main characteristic component of white matter. White matter being


  [the tissue] found in the deeper [in] the brain (subcortical). It contains nerve fibers (axons), which are extensions of nerve cells (neurons). Many of these nerve fibers are surrounded by a type of sheath or covering called myelin. Myelin gives the white matter its color. It also protects the nerve fibers from injury. Also, it improves the speed and transmission of electrical nerve signals


I think what the question aimed to target was your understanding what a myelin sheath is for (and, hence, what it is not intended for). Quoting from (Morell &amp; Quarles, 1999):


What 



  [A] greatly extended and modified plasma membrane wrapped around the
  nerve axon in a spiral fashion. [It] originates from and are a part of
  the Schwann cells in the peripheral nervous system (PNS) and the
  oligodendroglial cells in the central nervous system (CNS)



What for



  Each myelin-generating cell furnishes myelin for only one segment of any given axon. The periodic interruptions where short portions of the axon are left uncovered by myelin are the nodes of Ranvier, and they are critical to the functioning of myelin.



How



  In myelinated axons, the excitable axonal membrane is exposed to the extracellular space only at the nodes of Ranvier; this is the location of sodium channels. When the membrane at the node is excited, the local circuit generated cannot flow through the high-resistance sheath and, therefore, flows out through and depolarizes the membrane at the next node, which might be 1 mm or farther away []. The low capacitance of the sheath means that little energy is required to depolarize the remaining membrane between the nodes, which results in local circuit spreading at an increased speed. Active excitation of the axonal membrane jumps from node to node; this form of impulse propagation is called saltatory conduction (Latin saltare, “to jump”). Such movement of the wave of depolarization is much more rapid than in unmyelinated fibers. Furthermore, because only the nodes of Ranvier are excited during conduction in myelinated fibers, Na+ flux into the nerve is much less than in unmyelinated fibers, where the entire membrane is involved. 



What not
Although the myelin sheath is formed by a glial cell type, and although glial cells do structurally and metabollically support neurons, I would not say that this means myelinated tissue heals faster. Instead, myelin is more about the functional role of white matter, namely efficient, fast and reliable long-distance transfer of information across distant brain regions.    


Reference
- Morell &amp; Quarles. The Myelin Sheath. In: Siegel et al (eds); Basic Neurochemistry. 6th ed. Philadelphia: Lippincott-Raven (1999)