I doubt very much that Crossmarks are grippier than SB8s on much (if any) terrain, but they will probably be more resistant to sidewall tears.
SB8s are very grippy on hardpack, grippier than a Nevegal, and about as grippy as is possible for fine, loose terrain. When it gets wet they suffer quickly though.
They are my summer choice, but because they seem to behave quite differently to more traditional tread patterns I don't mix them with other tyres.
EDIT: Never ridden the Crossmark(!) so feel free to shoot me down, all based on experience of SB8s plus reviews of Crossmark etc.