Stain or overlay versus new decorative concrete
A stain or overlay makes sense when your old slab is still flat, solid and sheds water away from the house, because the coating only changes the top. If the slab is sinking, cracked clear through or pooling water by the foundation, I'll tell you to skip the coating, since it'll just follow the old problems. In that case put the money into a new base that's dug out and packed, and pick the fancier finish second, because nobody can fix the base after the pour.

