Acrylic is half the weight of glass. Glass tanks larger than 40 gallons get incredibly heavy very quickly. Acrylic aquariums are easier to ship, move and set up than heavy glass tanks.
Acrylic distorts much less and is more clear than glass. Acrylic aquariums are more clear and visually desirable than any kind of glass tank including "low iron" glass. In addition to having a slight green tint, most glass aquariums have an index of refraction that is considerably different from water. Clear acrylic has almost the same refractive index as water so there is no bending of light as it passes through the acrylic into the aquarium.
Acrylic aquariums look better with brighter colors and sharper shapes. The huge viewing windows in large public aquariums and oceanariums can be more than 12 inches thick but because they are made of acrylic, they afford a very clear view of the water and ocean life they enclose. The same is true for smaller home aquariums. Acrylic also allows better penetration of your system lighting, which is especially important for reef systems.
Acrylic insulates better than glass. Acrylic controls water temperature fluctuations, one of the primary reasons for fish stress, disease and death. Glass conducts heat and cold causing more fluctuations.
Acrylic seams are stronger than glass. Acrylic seams are molecular bonds and are stronger than the acrylic itself. Silicone seams used on glass aquariums dry out and weaken over time.
Acrylic seams are visually superior to glass. Acrylic seams are polished and nearly invisible. Silicone seams are clearly visible and have been known to discolor when exposed to certain fish medications.
Acrylic is easily refinished. If glass scratches (and it often does) it cannot be repaired. Acrylic can be repaired with a variety of scratch removal kits. Even internal scratches can be repaired without removing the fish from water.
Custom formed designs are possible with acrylic. Acrylic can be formed to create interesting aquarium designs which you won’t find with glass aquariums.
Acrylic aquariums are safer than glass. Acrylic aquariums can withstand substantially greater impacts than glass tanks.
Acrylic is the only option for large aquariums. Really big glass aquariums don't exist. The practical upper limit for big glass tanks is around 250 gallons. Anything larger is impractical due to the difficulty of moving and installation as well the structural weaknesses inherent in glass tanks.