What are actually the differences between Sidgwick & Powell theory and Nyholm & Gillespie Theory?
Perhaps you should read the original papers: N.V. Sidgwick and H.M. Powell, "Stereochemical types and valency groups", Proceedings of the Royal Society of London Vol 176, No. 965, pp 153-180 (1940), and R.J. Gillespie and R.S. Nyholm, "Inorganic Stereochemistry", Quarterly Reviews, Chemical Society 11 (4) 339-380 (1957).  

To quote out of Gillespie's paper:


  Sidgwick and Powell assumed that lone pairs of electrons and bonding pairs were of equal importance and that they arranged themselves symmetrically so as to minimise the repulsions between them. The ligand(or crystal)- field theory is concerned with the influence of the non-bonding electrons upon the arrangement of the ligands which are assumed to be negative ions or dipoles surrounding a central metal atom. Recently the influence of covalent binding has also been considered. These various theories are in fact closely related and an attempt has been made in this Review to integrate them. It appears that the simple theory of electron-pair repulsions receives considerable justification from quantum-mechanics and when refined to take into account differences between the repulsions between lone pairs and bonding pairs of electrons provides a very satisfactory theory of the stereochemistry of inorganic molecules.


That should get you going...