Temporal beam-shaping is a powerful tool for micromachining of various materials with femtosecond lasers. In this contribution, we present our advances of dielectrics microprocessing with an ultrafast laser source which can operate either in the MHz- or in the GHz-burst regime. We compare top-down percussion drilling in glasses with a Gaussian beam in both burst regimes. The GHz-burst mode allows for obtaining crack-free holes with an outstanding surface quality of the inner walls and featuring an almost cylindrical shape without shifting the beam focus nor the sample. The deepest hole is measuring 3.7 mm length and 25 µm entrance diameter, corresponding to an aspect ratio of 150, which is the highest reported so far with femtosecond GHz-burst drilling to the best of our knowledge. Moreover, we show a combination of temporal and spatial beam shaping for cutting of transparent dielectric materials. A Bessel beam is formed using an axicon, and we compare the cutting results in both burst operation regimes. We illustrate the influence of the laser beam parameters such as the burst energy and the pitch between consecutive Bessel beams on the machining quality of the cutting plane and provide processing windows for both burst regimes. In both regimes, dust- and chipping-free cutting has been achieved for glass samples of up to 1 mm thickness. However, the best cutting plane quality in terms of surface roughness is obtained in the GHz-burst regime.