In this article, in order to realize enhanced β-Ga2O3 metal-oxide semiconductor field-effect transistor (MOSFET) devices and increase their breakdown voltage, the gate-field-plate trench (GFPT) and the gate-mesa trench (GMT) β-Ga2O3 MOSFET are proposed. The breakdown voltage and power figure of merit (PFOM) of the GMT device are 2566V and 680.53MW/cm2 respectively, which are 1.56 times and 2.25 times of the GFPT device, and have excellent device performance. When the etching depth is 200nm, the specific on-resistance of the GFPT and the GMT are 8.84 mΩ·cm2 and 9.76 mΩ·cm2, respectively. When the epitaxial layer doping concentration is 3×1017 cm-3, the peak transconductance of the GFPT is 61.56 mS/mm, which is 1.22 times that of the GMT. The HfO2 medium with high dielectric constant can significantly increase the PFOM of the device, but the gate oxygen medium Al2O3 can make the threshold voltage drift more to the right. This article provides a new idea for the design of high-performance enhanced β-Ga2O3 MOSFETs.