Quote: '...as far as I'm aware there's no universal API.."
Actually there is, it's called OpenVR.
Developed by Valve, it currently supports both Oculus SDK, and the Vive SDK, and Valve have stated that if anyone else brings out hardware for PCs, they are happy to add their SDK to OpenVR as well, and have stated they will be working with the OSVR project (Open Source Virtual Reality).
OpenVR is on github: https://github.com/ValveSoftware/openvr
Boiler plate: 'OpenVR is an API and runtime that allows access to VR hardware from multiple vendors without requiring that applications have specific knowledge of the hardware they are targeting. This repository is an SDK that contains the API and samples. The runtime is under SteamVR in Tools on Steam.'
So if a developer uses the OpenVR API, it can work with Vive or Rift (although of course the dev still needs to take into account things like the difference in controllers etc).
Note that SteamVR is installed by the Steam client, but can be used by any OpenVR application on the PC, it's not restricted to Steam only apps. For example I have a none Steam version of Elite Dangerous (I was a KS backer), and that works fine on the Vive via SteamVR.
From what I understand, OpenVR was originally being developed for the Rift (before FB bought Oculus), back when Oculus and Valve were working together. After the FB buyout, Oculus decided to develop their own API, and not use OpenVR, and later decided to make that Rift specific only (Oculus have refused to add Vive support to their Oculus runtime).
So at the moment, if you develop for Oculus API, it's Rift only, and unlikely to ever support any hardware other than the Rift. Also all apps/game bought via the Oclulus store, will also only work on the RIft.
If you develop using OpenVR, it will work with the Vive, the Rift, and very likely any other VR devices in the future (headsets or controllers etc), with minimal (if any) changes to the application itself (perhaps an API refresh). And also Steam fully supports both Vive and Rift games and applications.