I have the 376
Which is the older sister of your boat. As of now, I am planning on crossing oceans with it but my change my mind once I get a few coastal legs under my belt. I've heard of a Hunter 34 doing that trip from Florida to Turkey. I would say that if you have bad luck, you better be a very good sailor though. The reason so many are against crossing oceans in Hunters are because if you have trouble in the middle of the ocean, help may be a few days away, so many want the strongest boat possible to do those types of trips and Hunter isn't that.The weaknesses on the 380 are the unprotected rudder, maybe the hatches and skylight, quadrant and emergency tiller (not big enough). The chainplates are solid but I can't comment on the rigging because that is done at the dealer, not the factory so you will want to pay extra attention to the rigging.You will have to make many modifications to ready the boat such as adding handhelds and latches on the floorboards and adding additional bilge pumps. Then you will not want to skimp on the safety gear (SSB radio, liftraft, flares, eprb, handheld vhf, emergency water maker, survival kit) because your changes of needed it are greater with a Hunter. Also don't forget the heavy weather gear you will need for the boat like storm sails and drogues and sea anchor.However, if you don't know anything about the weather windows, then don't go in a Hunter until you do and follow the window's advice...or get a different boat.