You can store the positions of the unit vectors in the eigensystems in a list, and then reorder eigenvalues and eigenvectors according to the position list:
posTableA =
Flatten@Table[Position[vecsA, N@UnitVector[8, i]], {i, 8}]
valsA[[posTableA]] == newvalsA
vecsA[[posTableA]] == newvecsA
posTableB = Flatten@Table[Position[vecsB, UnitVector[8, i]], {i, 8}]
valsB[[posTableB]] == newvalsB
vecsB[[posTableB]] == newvecsB
