The growing applicability of glass materials drives the development of novel processing methods, which usually lack comprehensive comparison to conventional or state-of-art ones. That is especially delicate for assessing the flexural strength of glass, which is highly dependent on many factors. This paper compares the traditional top-down laser ablation methods in the air to those assisted with a flowing water film using picosecond pulses. Furthermore, the bottom-up cutting method using picosecond and nanosecond pulses is investigated as well. The cutting quality, sidewall roughness, subsurface damage and the four-point bending strength of 1 mm-thick soda-lime glass are evaluated. The flexural strength of top-down cut samples is highly reduced due to heat accumulation-induced cracks, strictly orientated along the sidewall. The subsurface crack propagation can be reduced using water-assisted processing, leading to the highest flexural strength among investigated techniques. Although bottom-up cut samples have lower flexural strength than water-assisted, bottom-up technology allows us to achieve higher cutting speed, taper-less sidewalls, and better quality on the rear side surface and is preferable for thick glass processing.