If they updated the PC version to DirectX 9 then that would almost certainly carry over to the 360 version as well. Updating to DirectX 9 isn't about prettier graphics it's about eliminating glitches on modern PCs and better efficiency e.g. full shadows not slowing your system to a crawl. (although they could make it look nicer with some rendering tweaks).
If SE were to release a PS Vita version of FFXI they would have to recode the client for OpenGL because the Vita does not have DirectX (it's not a windows platform). And SE would have known this before even investigating the possibility. They must at least be willing to consider it or they would never have investigated it in the first place.