When two atoms collide, what determines whether they will react by transferring electrons or by sharing electrons?

If it is an ionic bond (metal with nonmetal) the electrons will be transferred. If it is a covalent bond (nonmetal with nonmetal) the electrons will be shared. It depends on the electronegativities; the closer the electronegativities of the two atoms, the more covalent the bond is, making the electrons more equally shared. But if the electronegativities are very different, one atom (the nonmetal) will pull the electrons from the other (the metal).