ABS and Acrylic are both types of plastic. Acrylic is more brittle than ABS, and ABS is a bit softer than acrylic.
ABS is typically very dark and Acrylic is typically transparent.
In the context of (our) number plates, ABS is a hard black backing, pre-layered with a reflective film overlaying the plate, where as our printed media is front applied over the reflective. Therefore the printed film (and therefore registration/design) is exposed on the front of the plate.
Acrylic, however, is a 3 layer manufacturing process where the printed film/media is applied to the back of the acrylic plate and a separate reflective layer then rolled on the back of the film. You are therefore viewing the printed film through the transparent acrylic plastic, meaning that the film isn't exposed. Although no contact at all is generally desirable, it means that if the plate is scratched or damaged, the acrylic takes the brunt of it rather than the film.
Both are BSAU (UK road) compliant, so ultimately it is down to individual preference as to weigh up the cost vs quality balance.