Vinca needs shade - buffalo grass needs FULL SUN.
Also need to differentiate between vinca minor and vinca major. V. minor is more preffered and well-behaved. And either are not to be confused with Vinca rosea (recently renamed to Catharanthus roseus), more commonly known as periwinkle (also called Madagascar periwinkle so as not to be confused with V. major or V. minor, which are both also correctly known as periwinkle!). V. minor (dwarf periwinkle or common periwinkle) and V. major (greater periwinkle) are also known as myrtle. I love Vinca minor as a ground cover, but I seem to see it not doing well in even part shade in these parts. I'm working on cleaning up a huge yard that is covered in V. minor. Cleaning out euonymous, english ivy, virginia creeper, honeysuckle, etc. The V. minor forms a nice even carpet under the shade of lots of large Easter Red Cedars (which are actually junipers!).
There may be many other options for that hillside, but buffalo grass would be a very interesting project. Just tonight I happened to be thinking that it would be cool if someone wanted me to plant a buffalo grass lawn. I think its expensive, but there is little or no maintenance once it is fully in - some people mow it a couple of time a year and some people never mow it. It would be great to see more of it around. But it does require FULL sun.......