The main advantages of liquid flux are one, that it is reasonably transparent and therefore will not obscure the solder seam during heating, letting you watch the soldering process closely; and two, it will flow more easily into solder joints than will paste flux. Liquid flux also has a wider temperature range (1100°F to 1700°F). Any flux forms a glaze on metal that acts as a barrier to air, and this prevents the formation of oxides that produce the darkening called fire scale. The wider the coverage of the flux, the greater the protection from fire scale. With relatively little coverage, however, liquid flux offers only minimal protection from fire scale.
