The SC series of boats have proven themselves capable of circumnavigations. Donna Lange is in the process of completing one in her SC 28. The two boats are very different, as the other posters have said here, and I think you really need to figure out what you want to get the boat for.
The Southern Cross 31 is a full-keel bluewater boat. It is going to be far heavier than the Hunter, and probably far slower, given the same conditions. However, in rough seas, the Southern Cross will likely be far more forgiving.
I wouldn't recommend getting a Southern Cross 31 as your first boat. Especially not one that isn't is ready-to-sail-away shape. Many new boat owners get a "fixer-upper" and get discouraged at all the work, since the boat isn't often sailable.
You also don't say what you intentions are for the boat, or what your budget is. If you don't have at least $7-10,000 set aside to fix up the Southern Cross 31, then don't even bother looking at it.
Don Casey says in his book This Old Boat, that many boat buyers generally pick the wrong boat as their first boat, and the lessons they learn from buying their first boat often mean that their second boat is one that they end up keeping for years, since they have learned what they are really looking for in a boat by then.
Older Hunters, with some exceptions, can be questionable in quality. It would help more if you said what vintage 27' Hunter you were looking at.
One other point on the Southern Cross... most of their boats had cored hulls, and if not properly maintained, run the risk of core breakdown and delamination.
If your goal is to learn more about sailing, and to have a boat you can daysail, and coastal cruise in for upto about a week at a time, then, I'd say get the Hunter. If you want to sail around the world or across an ocean, and are looking to get a boat that you can make into the perfect boat for doing so for yourself, and are willing to spend the next year or more modifying it and restoring it...then get the Southern Cross 31.
As a general rule, with used boats, it is often far more economical to buy one that is in sailable shape than to buy a comparable boat that is not and refurbish it. The price difference is often just a small fraction of what the refitting or repairing would cost.