The same molds have been used/released by Gallery and Trumpeter as well - sort of a partnership deal. The two main releases have been Wasp (Gallery and Revell) and Iwo Jima LHD-7 (Gallery and Trumpeter). The kits themselves were largely designed by Trumpeter.
There are some differences between the two kits because there are differences between the ships. The Iwo Jima kit is an easier starting point as she is closer in configuration to the Bataan. Another proud papa built a Bataan for his son with a good build log here that might be of use - the finished build has been posted as a gallery here.