The physical difference between high- and low-mass X-ray binaries is that the latter has a donor star that fills its Roche lobe. Usually, the compact object is more massive than the donor star. Mass transfer occurs via Roche lobe overflow.
In high-mass X-ray binaries usually the donor star is more massive than the compact object and mass transfer is via a stellar wind.
The reason that a disc may form (in either case actually, but almost always for a LMXB) is that there is too much specific angular momentum (angular momentum per unit mass) in the accreted material to allow it to fall directly onto the compact object (angular momentum must be conserved). Broadly speaking, a condition for the formation of an accretion disc would be that the specific angular momentum of the accreted material exceeds the specific angular momentum of material in a Keplerian orbit at the surface of the compact object. The formation of an accretion disc would be favoured by short orbital periods or slower wind speeds. Material can then only be transferred onto the compact object as angular momentum is transferred outward by (possibly) viscous torques.
This simple picture is immensely complicated by the presence of any strong magnetic fields.