Two Multigap Resistive Plate Chambers (MRPCs) were built with thin (0.4 mm) low-resistive glass sheets for the inner plates and standard 0.28 mm ‘soda lime’ float glass as external plates. The 6-gap MRPC reaches 96.5% efficiency at 15.6 kV and a time resolution of 68 ps at an instantaneous particle flux around 2.5 kHz/cm2. The 20-gap MRPC reaches 98% efficiency at 18.8 kV and a time resolution of 32 ps. Compared to a 6-gap MRPC built previously with all plates made with soda-lime float glass, the two MRPCs made with low-resistive inner glass show a much higher count rate capability. A third MRPC with all plates made from low-resistive glass was also constructed to verify the operation at high particle flux. In this paper a relative rate capability comparison between the MRPCs has been performed under a pulsed beam with a small spot on the chamber. Their rate capability under full illumination with continuous particle flux needs to be further studied.