Wilson:
You hit the nail on the head, when you mentioned issues with the older type clasp. According to someone that I spoke to at the Patek Boutique, they had problems with the "Chevron" clasps. I was told that the either broke or opened causing the watch to fall off the wrist and damaging the watch. Those unfortunate people were compensated for their damage.
Mark
I have one of each and prefer the look and profile of the Stern clasp to the Calatrava Cross clasp. The former lies flush with the strap, while the latter protrudes a bit. I'm unaware of any functional difference.
Park
I have also owned both types of clasps and in my experience the cross clasp was not best suited to fit my smaller wrist, as it didn't lie flat on my wrist.
Which on several occasions led, to me catching the clap on furniture as I walked past, thus causing the clasp to open.