Vulcan is better option, because it would be a common way of programming for PC, XBox and PS.
That is not very true...
XBox is DirectX. It is after all Microsofts console, so why would they use a competing API?
Playstaiton, uses their own API, GNM/GNMX, they have used OpenGL implementations before (PS3), but it was not very used, so it got removed in PS4, why put in the effort for a limited use API on their platform? There are some indication that Playstation 5 might support Vulkan, but that still leaves PS4 out...
So unless you intend to use some kind of wrapper to use Vulkan and then translate to the other "native" API on the consoles, you are going to have to implement
GNM/GNMX and DirectX at minimum regardless
On PC we can use DirectX and OpenGL/Vulkan, but not GNM/GNMX , so it makes sense to reuse the DirectX from XBox on PC, instead of adding a 3rd API to the mix
We used to have OpenGL support in the Mac version of Elite, but since Apple decided to dump OpenGL in favour of its own Metal API, so that was the end for Elite on Mac, to few users to warrant the rewrite.
So on Linux, we have OpenGL/Vulcan, but with Proton/Wine etc we also have DirectX.
So a bit about Elite on Linux, it works with Proton, and the biggest hurdle seems to be to get the launcher running! and this seems to be caused by the use of dotNet... so a new launcher that is much more Linux friendly could be make it alot easier to run on Linux. And if the game would upgrade to use DirectX 12, then any performance difference between native Linux client using Vulkan and Windows client using Vulkan or DX12 should be minimal, and often the Windows client tends to be more optimized than the Linux client, so it has not been unusual that in such situations the Windows client have been faster than the Native Linux client! Where difference start to show in favour for Linux is when we are hitting 200+ FPS using DX, at which point, for a game like Elite, makes very little difference... and if we start to extrapolate how many of the Elite players on Linux using a 200+ FPS capable monitor, and we are talking about a very small subset of the Elite player base...