Are we talking about straight arm or bent arm pullovers? If bent arm pullovers, than using DB's with a hammer grip would lessen the tension on the elbows, forearms and wrist. BB's may be too fixed and awkward for most, giving too much unneeded strain. When working into some respectable weight with the straight arm version, tension on the elbow joints will be more. Sometimes if the hands are placed too wide on the bar, shoulder or elbow stress can occur. Want a narrow grip at all times.
Your not going to mimic or gain all the benefits of the full lying horizontal stretch (BB or DB) with any chinning style, cable or whatever could give (lats, pecs/rib box, triceps and even the abs stretch). Only exception would be an Art Jones type of pullover machine, where you have to jam yourself into it at first. You want the weight pull/stretch forcing the arms/hands back & down (like behind the head) towards the floor, not just out and away from the body like a cable movement. With the bent arm version (as with a pullover type machine) the elbows will lead the motion, which is what you want.
If I had only time for one upper body exercise it would be the bent arm DB pullover and press. A true mass builder. The serratus is hit strongly by any over head pressing, including high angle inclines. The bench and chins/lat machines also. Good Luck.
