Why would you use the straight jaw more often? I thought the V jaw is a better grip. Apparently, the V jaw is CL's take on the Knipex design. Why is it better on Knipex but worse for CL?
I feel like the subtext of your questions in this thread is hinting that you want to buy one set or the other and are wondering if you ought to spend the extra $7 for the straight jaw vs. the V-jaw.
I think it depends on what type of work you do most. I'm usually doing mechanical-type jobs and the straight jaw is usually what I reach for. If you do electrical or plumbing work, I think the V-jaw makes more sense. V-jaw wraps around for extra contact on round objects. It's also narrower and skinnier top to bottom.
HOWEVER, even if I have a preference for certain tasks, I bet > 90% of the time I could get the job done with either. They are just variations of a similar tool. It's like the difference between straight-jaw or curved-jaw locking pliers; different, but very similar.
If I'm pulling on something, I'd rather have the straight jaws. Also my preference for squeezing a brake caliper piston back in. Holding something while I heat it with a torch or grind it? Straight jaw. However, if I have room to wrap around something to spin it - I'd grab the V-jaws. Same thing for holding round objects.
Channellock also makes "Speedgrip" pliers if you want something closer to Knipex Cobras. They are a bit more expensive though.
Even metaldad, who does NOT buy gimmicky pliers, has a pair of V-jaw pliers that have snuck into his collection (they're in the bottom row, to the left side of his 909 crimping pliers and underneath a pair of straight jaw pliers).