The antenna design of the Verizon iPhone was tweaked slightly to work on the carrier's CDMA network. It was not, however, tweaked enough to totally eliminate "antennagate" issues.
iLounge has done some hands-on (no pun intended) testing of the Verizon iPhone, and managed to duplicate the "death grip" issue of the AT&T iPhone 4, where holding the iPhone 4 in the "wrong way," bridging the gap in the lower left hand side of the phone caused signal attenuation and data slowdown. That issue eventually brought free cases to all for a time, and still continues to allow free cases on a (once again, no pun intended) case-by-case basis.
However, iLounge also managed to duplicate something it had been warned about prior to the Verizon iPhone launch, which it called the "death hug." Holding the phone in both hands and in landscape mode, with wi-fi on, data transfer is slowed dramatically. To be clear, this is when the device is transferring data over wi-fi, not 3G.
Both scenarios are visible in the video below. Both are also fixed as in the AT&T iPhone 4: any type of case.