The operation of 1-3 nm thick SOI MOSFETs, in double-gate (DG) mode and single-gate (SG) mode (for either front or back channel), is systematically analyzed. Strong interface coupling and threshold voltage variation, large influence of substrate depletion underneath the buried oxide, absence of drain current transients, degradation in electron mobility are typical effects in these ultra-thin MOSFETs. The comparison of SG and DG configurations demonstrates the superiority of DG-MOSFETs: ideal subthreshold swing and remarkably improved transconductance (consistently higher than twice the value in SG-MOSFETs). The experimental data and the difference between SG and DG modes is explained by combining classical models with quantum calculations. The key effect in ultimately thin DG-MOSFETs is volume inversion, which primarily leads to an improvement in mobility, whereas the total inversion charge is only marginally modified.