Dear Mal,

RM1 is a  semiempirical molecular orbital model capable of modeling most molecular systems of importance to organic chemistry, biochemistry and pharmaceutical research. Essentially identical to the AM1 method, but with improved performance - with much newer and better parameters. In most cases, RM1 yields superior results to both AM1 and PM3 - for organic and biomolecules.

It is Not surprising that the results from RM1 and DFT are different because the parameterization of RM1 is not the same as for DFT.

Parameterization for RM1

RM1: a Reparameterization of AM1 for H, C, N, O, P, S, F, Cl, Br, and I

Gerd Bruno Rocha, Ricardo Oliveira Freire, Alfredo Mayall Simas*, and James J. P. Stewart. Journal of Computational Chemistry 27(10), 1101-1111, 2006.

Parametization for DFT:

Hybrid functionals are a class of approximations to the exchange–correlation energy functional in density functional theory (DFT) that incorporate a portion of exact exchange from Hartree–Fock theory with exchange and correlation from other sources (ab initio or empirical). The exact exchange energy functional is expressed in terms of the Kohn–Sham orbitals rather than the density, so is termed an implicit density functional. 

Hoping this will be helpful,

Rafik