Since no one else answered I'll take a stab at this. Marine biology isn't my forte. I think both schools have good marine biology programs. UH is known nationally for its marine biology program and the work it does out at Coconut Island in Kaneohe Bay. Here are two links.
Hawai‘i Institute of Marine Biology | Welcome
HIMB Shark Lab
I studied at UHM as an undergraduate. I took some oceanography classes where we did work at Coconut Island. It was a great experience. However, HPU has the Oceanic Institute which I think is their research facility. My co-worker's daughter is a marine biologist. She says that one has to have a graduate degree to get a job in the field. As far as I know, HPU doesn't offer graduate degrees in marine biology. UH does as part of its oceanography program.
As for general info comparing the two schools ....
HPU is a private college though not as expensive as some private colleges. It really doesn't have a college campus feel. They have a "college" in Downtown Honolulu which looks just like any other office nondescript building in Downtown Honolulu. There's also a windward campus which is in a nice green area off the Pali Hwy. It sort of resembles what one might expect of a college. They also have the previously mentioned Oceanic Institute.
According to the US News & World Report's 2010 edition, HPU has a higher freshman acceptance rate. It also accepts lower SAT/ACT scores than UH. It has a more generous financial aid package for students. It's a private school so the teacher student ratio is smaller. You'll get to know people better.
UH is the state university. It has bachelor's, graduate, and post graduate programs. HPU doesn't have a PhD program. UH tends to attract more local high school graduates than HPU. UH has a higher graduation rate and more full-time faculty. There are more students and more classes available at UH in comparison to HPU.