Might be smart to check with your AHJ. Some towns specify one pipe and prohibit the other. Other towns allow either.
I can't say if this is true or not, but a common belief is that PVC can muffle the sound of water a bit better than ABS, so that can be good for DWV, especially for muffling toilet waste.
PVC needs a primer and when the primer is dry, then glue. ABS just needs to be glued.
Mixing the two? Using ABS-PVC solvent glue is not a code-approved option for in-house residential construction. Use a coupling hub, which a previous posted recommended. To meet code the coupling should be UPC approved, meaning it will have the UPC trademark on it. The trademark looks like a small shield (think shield as in 'sword and shield' like in the movie Braveheart) with 'UPC' on the face of the shield. The better couplings have stainless steel ring clamps on each end, with stainless straps running the length of the coupling to provide rigidity across the joint when it is made up.
Will ABS-PVC glue work? Will a non-UPC approved coupling work? Yes. But you might get dinged in an inspection when selling the place. Or if you do some sort of permitted work down the road and when inspecting that the inspector happens to see an ABS-PVC hybrid system, the inspector might look at everything with a more critical eye.
Good luck!