I think the answer really depends on how many images you will need to do, and how big the files are.
My wife was in Antarctica for two months this past winter, but was on an icebreaker, so no concerns about being away from the computers for too long. She is also not a photographer, but she did take a lot of images and stored the files on the laptop with an external HD as the backup. Once there and confirmed, she deleted the cards and reused them.
For 3-10 days, I would probably plan on a single computer in the field, and enough cards for the entire time (in the field). Then, back at McMurdo, an external HD box with a normal HD in it. If you don't think you will have the room on the computer for the full trip, you'll need a second external HD as a backup. Do not do a RAID box! Do two separate HDs in two separate enclosures, and make sure you get reliable products with good shock resistance.
Do you need the computer for other purposes? That may affect the answer.
I would choose the computer based more on whichever one was most likely to survive (in a ruggedized case like a Pelican, of course). That does support going for SSD in the machine.
---Michael