I am replacing basement receptacles with GFCI outlets. I have armored cable with only a white and black wire-no ground. Is that a problem? Is it necessary to use the stab in receptacles or does it make a difference just using the screws on the side?

The armor may be the ground, needs to be intact, and with boxes.
If it is the stabbing/then tighten screw type, stabbing works fine for stranded.
Solid wire can twist even when tightened, the around screw would be best.
I never backwire regular recepticles.