This paper demonstrates a systematic comparative study on the mid-infrared laser performance of Er∶YSGG crystals with thermally bonded, concave end-face, and different diameter. After annealing at high temperature, orientation cutting, and precision polishing on the end face, the flatness and surface roughness are less than 0.1λ@633 nm and 0.5 nm. The room temperature optical glueing of YSGG and Er∶YSGG was realized by the precision machining, and then high temperature thermal bonding was carried out. The transmission spectra show that the bonded interface is basically integrated without loss. The thermal focal length shows that the thermal lens effect of crystals at high power pumping condition is improved and compensated efficiently by thermal bonded and concave end-face, which are beneficial to improve the laser performance of crystals. Compared with non-bonded Er∶YSGG, the laser performance under 968 nm LD side-pumping method of bonded and concave end-surfaces Er∶YSGG crystal do not show advantages at low frequencies below 150 Hz, the maximum output power and slope efficiency of the three crystal rods all are about 24 W and 28%, respectively. However, with the increase of repetition frequency, the thermal effect gradually increases, and the laser performance of bonded and concave end-face crystals is improved due to their perfect heat dispassion and concave thermal compensation effect. Under the repetition frequency of 300 Hz, the maximum output power of non-bonded, bonded and concave bonded rods is 15.54, 17.85 and 18.33 W, corresponding to the slope efficiency of 16.6%, 18.3% and 18.4%, respectively. Under the repetition frequency of 600 Hz, these rods maximum output power and slope efficiency are 9.4, 13.32 and 13.18 W, 6.7%, 8.6%, and 9%, respectively. In addition, the laser properties of Er∶YSGG crystals with different diameters are studied, and the laser properties of these three crystals are similar under the low frequencies below 100 Hz. However, compared with the 3 and 4 mm bonded concave rods, the 2 mm diameter rod possesses a larger specific surface area and better thermal management capability, which is beneficial to improve the laser performance. For example, at 150 Hz, a maximum output of 23.82 W is obtained with a slope efficiency of 27.7% by Er∶YSGG concave bonded crystal rod with 2 mm diameter, which is much higher than 18 W and 23% that is achieved with the 3 and 4 mm crystal rods. Besides, by using a concave bonded rod with 2 mm diameter, the maximum output power of 13.18 W is achieved with a slope efficiency of 9% under the higher repetition frequency of 600 Hz, which is better than that of 9 W and 7% for the concave bonded rod with diameter of 3 and 4 mm. The beam quality factor M2x/M2y of Er∶YSGG laser is measured by using 2 mm concave bonded crystal rod at 150 Hz, 200 μs, the values are 6.28/6.30, which indicates that the laser has good beam quality. In conclusion, choosing an appropriate crystal rod diameter and combining bonded with concave surfaces effectively achieve high-performance 2.79 μm lasers.