I am sure Jeff H will have some good comments on this thread too, but here are my OPINIONS (just mine)...
Some boats really are built better for offshore sailing. THey have the right tankage, lots of handholds, are tighter (making moving around in seas easier), have fewer (and generally smaller and stronger hatches), and most of the gear is "oversized" compared to what we would call a coastal cruiser. There are many other things I will not go into.
All that being said, I would have no problem taking a properly equipped Catalina or Beneteau or Jeauneau offshore (and have done it many times). I know of one gentleman particulairly that has had his 36 to South America and circled the Statue of Liberty (with several stories of 20+ foot seas). Would I take it to Hawaii? Yes, but I would be pretty careful about weather windows, etc. I would prefer a Valiant or Mason or other good offshore boat.
I think it was Hello?? that said to buy the right boat for the right thing?? Very true. Many of us have said that many times. You really cannot make a Catalina into a Valiant, as it will always be stronger (plus it would be cost prohibitive). That DOES NOT MAKE A CATALINA A BAD BOAT... just better designed for island hopping. It has lots of room, lots of "airy" hatches, and is very comfortable down below. My only comment to that is most of the boats which are "offshore circumnavigators" never make it past the first marker... for reasons that are a whole other thread.
Big fat boats with wide beams and few handholds (I always add more) can be a real bruiser offshore... especailly in a breaking sea. I know this from experience. But when you get to the anchorage, and drop the hook, it sure is nice to have all that room!!
Thus, if you really are planning on circling the globe, don't try and make an island hopper into a circumnavigator. I will also say that if you are planning on primarily Island hopping, don't try and make a circumnavigator into a fat comfortable liveaboard!! (Just my opinion, I am not trying to pick a fight with anyone). Buy your boat for how you will use it 99% of the time.
If you want both, break out the checkbook and go buy a Nordhavn. Putting a sailing dinghy on the back so you can still call yourself a sailor!!