In the gi, I only use a cross grip on their sleeve. It allows me to create a figure four grip with my hands over their wrist, and then use that to break any grip they have on my gi and work from there.
In no gi, I'll use both.
With the no gi cross grip, I'll grab across so that my index and thumb are around the bony part of their wrist and the rest of my hand is grabbing their hand. The same side hand cups their triceps from the outside, with the index and thumb gripping right above the bony protrusion of the elbow. This is my slow arm drag grip. I'll be using it to work a modified 2 on 1 to the closed guard arm drag position for pendulum sweeps, back takes, and arm bars.
With the no gi same side grip, I just use the same side hand to stiff arm their wrist in, and the cross side arm cups the triceps from the inside. This is my quick arm drag grip. When I do it, I'm coming up right away.