It is a very good question and a point of research. I think I would do a literature search on this topic to determine how differences in the spectral responses between ETM+ and OLI data might affect spectral vegetation indicies. For example:
http://www.sciencedirect.com/science/...
http://www.mdpi.com/2072-4292/6/1/310...
https://www.researchgate.net/file.Pos...